Tournaments are different from cash games, like they are different from non gambling practise games. A lot of people start to imagining that the chips mean something different from what they are. Betting all your chips to get someone else's chips is not the best idea and turns your betting strategy into a mess.
Tournaments are a special type of poker that needs a new take on rules. There will be lots of time to go all-in. But there are times when you may want to stay out of the line of fire. If more than one person is going all-in, perhaps someone with a short stack and they are getting desperate it is not a good idea to go in as well unless you are sure you have a good hand. Here is why. One person is going to lose, the other is going to have a lot more chips, but the more people that go all-in there is less of a chance that any one player will win the pot. Sounds complicated but really no matter what you hold, there are lots of combinations that will beat it. Most times people go all-in before the flop so you can't be sure of the cards and you are essentially gambling at that point. If it's the first few rounds with a set of brand new people, don't think that being macho will help you against good cards. Those players going all in are hoping to double up very quickly and that does pay off, but over time that kind of thinking leads to bad decisions and eventually those will cost you the tournament. The best players build chips slowly without the gambling.
The time I find to go all-in that matters the most is not on the flop but on the river. By then, you have seen all the cards and the other person - usually only one has a real hard decision to make about your cards. You can make them back down or you can maximize your pot win by waiting till the end. Or you go out knowing you had a good hand. Going all-in on a bluff doesn't work all that well so don't try that too often.
One thing to remember is timing. The bad decision players will drop out at the beginning so you need to remember not to be too fast to bet. Take your time. While you are prolonging your game, the other players are exiting and you can give yourself a better chance at making the final table by being patient alone. Chip counts will go up and down, and you will make some good and bad decisions, but you can control the time you play. I have had a good lead on some wild gamble bets, even been chip leader, and then went out making bad call after bad call. On the other hand, when I went all-in with a desperate small stack, I won three hands in a row and came back up to par with the other players. I was so determined that I had lost, I had signed up for another online tournament and was playing both at the same time; watching me lose the second tournament while the first one went on for another table or two. So timing and patience is a bigger virtue in tournaments than at a cash game. When you hit the end of your stack in a cash game you are finished, but wasting chips faster in a tournament puts you out faster.
Friday, April 30, 2010
Sunday, April 25, 2010
Poker Tactics - Player Behavior
Poker is a game that combines many disciplines to play well and win. How many sports rely on an almost psychologist-like ability to understand a person and think fast about their true intentions? The strength of your cards is well known in poker, and that doesn't change. The ability to spot a trap is what separates the winners from the losers on bleachers watching the action.
The ability to sum up an opponent is an art that requires some science - theories and observation - and what better way than to watch the cards and watch the bets. You get to see the cards that win, and sometimes the cards that lose to get some insight on that person. Perhaps they were hoping for a gut-shot card; that tells you something.
Of course, claiming that a person is a certain way based on how they playing right now is silly. Sometimes people vary how they are playing. So to assume that what you are seeing is how they really are all the time is foolish. Daniel Negreanu argues you should vary your play a lot - and he is very successful at poker. Phil Ivey may have won more tournaments but Daniel is the all-time money leader for a reason. So that is the prime reason why you don't want to analyze endlessly how someone played one hand. You are wasting your time on the wrong thing in my opinion.
I argue that reading someone has little value past the time you are playing. In fact, I try not to remember how they played since this time it might be different. So what I am proposing is that you study the player at the time and recall a little of how they played before. Discount the history and understand how they play right now in the tournament or cash game they are in.
So based on my experience I have classified the type of players you will face. Here is my working knowledge of the different personalities - it is not complete and not perfect but it is a start.
The ability to sum up an opponent is an art that requires some science - theories and observation - and what better way than to watch the cards and watch the bets. You get to see the cards that win, and sometimes the cards that lose to get some insight on that person. Perhaps they were hoping for a gut-shot card; that tells you something.
Of course, claiming that a person is a certain way based on how they playing right now is silly. Sometimes people vary how they are playing. So to assume that what you are seeing is how they really are all the time is foolish. Daniel Negreanu argues you should vary your play a lot - and he is very successful at poker. Phil Ivey may have won more tournaments but Daniel is the all-time money leader for a reason. So that is the prime reason why you don't want to analyze endlessly how someone played one hand. You are wasting your time on the wrong thing in my opinion.
I argue that reading someone has little value past the time you are playing. In fact, I try not to remember how they played since this time it might be different. So what I am proposing is that you study the player at the time and recall a little of how they played before. Discount the history and understand how they play right now in the tournament or cash game they are in.
So based on my experience I have classified the type of players you will face. Here is my working knowledge of the different personalities - it is not complete and not perfect but it is a start.
- Aggressive - the aggressive player pushes the limits of playing. Aggressive bets a lot without a sure hand in his mitts. They run up the pots and this turns on them most times. The best way to beat them is to call behind their bets - when you have a good hand, and let them raise the pots. Because aggressive people aren't believed they tend to get others to play weaker hands trying to simply beat them with a pair. Just stay in the wake and let them do all the work. Then you turn your cards and make em weep. Of course, you need to watch for other good players using them as a shield too.
- Bluffer - the bluffer thinks you can bluff your way to win instead of holding good cards. This kind of player plays all kinds of cards and you can't predict well what kind of cards they have. So betting against the bluff does not always payoff. Bluffing against a bluffer won't work because they are trying to convince you of the same thing.
- Conservative - These players play only the premium hands; AA, AK, KK, AQ, and suited pairs. They are not here to gamble, they are going to play when they have a hand. They might play suited connectors but they like to play only when they know they have a good hand on the outset. This is a good opponent, because you know that if they have a good hand you need to get a good flop or you should fold. Because they play fewer hands, they try and maximize the winning hands. This is their undoing. I beat a conservative with 7 8 and the flop came up 9 10 J making the straight. I had that AK beat from the start, and it was a predictable outcome. He could not accept that he was beaten and he drove to the river. A King came up and sealed his fate because that's the system and he couldn't see the end. They are predictable, so use this knowledge wisely. But if they re-raise and you didn't get the good flop then get out, get out fast. Bluff work well against conservatives if they didn't get the flop or they are uncertain if you can beat their AK.
- Unsure - the unsure player looks like all the other players from time to time. Unsure wants the cards to go a certain way, or perhaps raises / bluffs to see the flop and instead of re-betting then checks and folds. Once you see a pattern that makes no other sense then perhaps that person is unsure of what strategy to take. This can be a hard player to figure out because they are unpredictable. If you think this player is inexperienced then you can take advantage of their bad card knowledge from time to time. But proceed with caution and expect that sometimes they will luck out on the river.
- Dangerous - this is the kind of player to watch for. You will know that you ran across one of the dangerous ones if you lose half your chips and still can't figure out what happened. These players vary their strategy on purpose. They know the good hands and they play the good odds. And they have figured out all the other player behaviours and how to play against you no matter what the cards are. These are the players to avoid. If you run across one of these and you don't want to lose lots of chips then fold that good hand or follow my conservative policy - flop-then-out: play until the flop and get out unless you have a solid win hand like full house or a straight don't wade into a betting war with a dangerous player. I would recommend that when you are starting out to stay away from any player at the table that can bust a player or several players in a single hand. They might have been lucky - and that's just what they want you to think.
Poker Tactics - Stack Management
There are only so many chips you can have. And poker has a way of making them go up or down a whole lot in a little time. I have started with $20, won enough to make $40, and then back down to $5 without much consistency.
Another art in poker is knowing when to say when. The most important factor is what kind of poker you are playing. And of course if you can't afford to lose the money then don't sit down in the first place.
If you are playing in a tournament, and I have won a tournament, stack management is not a problem at the beginning. The fact is that stacks don't really matter until the later rounds so you should not be too concerned with your stack getting low at the beginning. You are going to lose some chips along the way, perhaps even all of them with a re-buy, but you have to remain to the later rounds to win. A good hand to go all-in with can settle your chances in that tournament or not. So you need to risk it from time to time. In fact, when you are playing a tournament I would recommend that you go after winning hands at the beginning when the blinds are smaller so you do have a chance of winning and taking out some players. So you should not worry too much about losing some chips when you have a chance to eliminate players yourself. That does not mean chase bad hands and lose, it means take a risk on a medium strength hand now and again and you will have more chances to win. In fact, betting on an odd ball hand like pocket fours and then a good flop comes up is just the way to beat someone playing Ace King or pair of Aces.
If you are playing a cash game, I would be ultra conservative. I would start with your original total and stop if you get just below half of what you came to play with. If you lose more than half your chips, and you are a good player it should tell you something. You might be getting no help on the flop - and that goes in streaks and you should accept that - in which case you will have a harder time winning them back. It could also mean you are making bad decisions on hand strength, in which case you could be tired or not concentrating and then you are not playing poker you are just donating your money. It could also mean that someone at that table has figured you out so you better leave - leave very fast - and take a break.
If you want to control the speed at which your stack increases or decreases there is a simple rule. Stack size varies with how good a hand you decide to play. If you play lots of medium strength hands instead of just the very good hands then your stack size will go up and down. If you play only the best hands then your stack size will stay the same, dipping at one time or another, and then you can control the stack size easily.
There is a simple reason for this rule. The way to play poker is easy, you will learn most of the tactics, table talk, and betting behaviours in a few days at most. The betting will make sense when you succeed and fail when your bets become won pots and when your bad bets become loses. So then there is no real mystery. Once you learn that you will win and lose at the right times, sometimes lose at the wrong times, and so you will win chips and lose chips with regular frequency.
Good hand strength doesn't change. Only the flop changes and that is what varies whether your bet was a good one or not. As I discuss in my other post about cards, there are really only three ways to win most hands. Straights, sets, and flushes. So there is little to master in term of difficult skills or hard concepts. Chasing riskier hands means you are going to slowly lose chips. Betting on only the best hands means you will only play the best hands and you will probably win those hands - not all - and so your stack size will stay the same and you will do a lot of waiting.
If you are playing a tournament, then of course your goal is to get all the chips and so you need to be aggressive from time to time and that will mean going all-in to win it all. You need to have patience, and you need to play good cards with the occasional bluff thrown in for good measure.
If you are playing a cash game on your own money, then I would live by the rule of two. If you chips get below half - quit. If you double your money, then start to play conservatively or quit. I have given back more money with the ups and downs of playing medium hands so I can assure you that it's not fun to lose those winnings. If you need to, make a new marker with you winnings to avoid giving it all back. For example, if you start with $20, win up to $35, and then start to lose then perhaps you should think about stopping when it gets to $30. A 50% return on your money investment - not time since I am sure you are worth more than $0 / hour- is a good day at poker.
Playing when you are desperate to win it all back in a hurry is the worst way to play. The more you are desperate then how likely are you to spot the traps and avoid them? Poker is a discipline, and the best players know when to fold more than they do know how to bet on winning hands. Any idiot can raise with pocket Aces, it takes an artist to check-raise and sucker people into a straight. But if you are worried about losing a few chips to make a larger pile then perhaps you need to take up another sport. Poker stacks don't matter during play, they only matter at the end when you leave.
Another art in poker is knowing when to say when. The most important factor is what kind of poker you are playing. And of course if you can't afford to lose the money then don't sit down in the first place.
If you are playing in a tournament, and I have won a tournament, stack management is not a problem at the beginning. The fact is that stacks don't really matter until the later rounds so you should not be too concerned with your stack getting low at the beginning. You are going to lose some chips along the way, perhaps even all of them with a re-buy, but you have to remain to the later rounds to win. A good hand to go all-in with can settle your chances in that tournament or not. So you need to risk it from time to time. In fact, when you are playing a tournament I would recommend that you go after winning hands at the beginning when the blinds are smaller so you do have a chance of winning and taking out some players. So you should not worry too much about losing some chips when you have a chance to eliminate players yourself. That does not mean chase bad hands and lose, it means take a risk on a medium strength hand now and again and you will have more chances to win. In fact, betting on an odd ball hand like pocket fours and then a good flop comes up is just the way to beat someone playing Ace King or pair of Aces.
If you are playing a cash game, I would be ultra conservative. I would start with your original total and stop if you get just below half of what you came to play with. If you lose more than half your chips, and you are a good player it should tell you something. You might be getting no help on the flop - and that goes in streaks and you should accept that - in which case you will have a harder time winning them back. It could also mean you are making bad decisions on hand strength, in which case you could be tired or not concentrating and then you are not playing poker you are just donating your money. It could also mean that someone at that table has figured you out so you better leave - leave very fast - and take a break.
If you want to control the speed at which your stack increases or decreases there is a simple rule. Stack size varies with how good a hand you decide to play. If you play lots of medium strength hands instead of just the very good hands then your stack size will go up and down. If you play only the best hands then your stack size will stay the same, dipping at one time or another, and then you can control the stack size easily.
There is a simple reason for this rule. The way to play poker is easy, you will learn most of the tactics, table talk, and betting behaviours in a few days at most. The betting will make sense when you succeed and fail when your bets become won pots and when your bad bets become loses. So then there is no real mystery. Once you learn that you will win and lose at the right times, sometimes lose at the wrong times, and so you will win chips and lose chips with regular frequency.
Good hand strength doesn't change. Only the flop changes and that is what varies whether your bet was a good one or not. As I discuss in my other post about cards, there are really only three ways to win most hands. Straights, sets, and flushes. So there is little to master in term of difficult skills or hard concepts. Chasing riskier hands means you are going to slowly lose chips. Betting on only the best hands means you will only play the best hands and you will probably win those hands - not all - and so your stack size will stay the same and you will do a lot of waiting.
If you are playing a tournament, then of course your goal is to get all the chips and so you need to be aggressive from time to time and that will mean going all-in to win it all. You need to have patience, and you need to play good cards with the occasional bluff thrown in for good measure.
If you are playing a cash game on your own money, then I would live by the rule of two. If you chips get below half - quit. If you double your money, then start to play conservatively or quit. I have given back more money with the ups and downs of playing medium hands so I can assure you that it's not fun to lose those winnings. If you need to, make a new marker with you winnings to avoid giving it all back. For example, if you start with $20, win up to $35, and then start to lose then perhaps you should think about stopping when it gets to $30. A 50% return on your money investment - not time since I am sure you are worth more than $0 / hour- is a good day at poker.
Playing when you are desperate to win it all back in a hurry is the worst way to play. The more you are desperate then how likely are you to spot the traps and avoid them? Poker is a discipline, and the best players know when to fold more than they do know how to bet on winning hands. Any idiot can raise with pocket Aces, it takes an artist to check-raise and sucker people into a straight. But if you are worried about losing a few chips to make a larger pile then perhaps you need to take up another sport. Poker stacks don't matter during play, they only matter at the end when you leave.
Poker Tactics - The Art of Bluffing
There is one thing that is really misunderstood about bluffing by most people that don't play poker is that bluffing is a big part of the game. It isn't. You can't scare someone with good cards away with bluffing - in fact, they are most likely to appreciate you running up the bets while they get ready to win. Bluffing is when you pretend to have a better hand, most times by betting on bad hand, and it only works if people with better cards give up their cards and let you win. Of course, sometime people bet on speculation that the next card will be better, that is still a bluff when you don't have the cards to begin with. For any bluff to work it needs to be believable and so you need to understand it.
Bluffing takes skill and it takes some luck. In fact, I would argue bluffing only works in one case. When you are winning. You may get lucky by position when you bet on a hand and you are hoping for a card and someone mistakes your bet for a good hand already. Or if the other players have shown their weakness by checking, and then you raise you may fool beginners and you may scare off experienced players.
But I have found bluffing only works, in general, when you have been winning and the other players are scared that you have got them again. I can remember a time when I had a pair of fours, hole cards, and I was running up the bets on a table. I made most of them quit - except the eventual winner that had two Kings - because I had won some monster pots before that. I almost made him give up two kings because I had beaten them all in recent history with some lucky hands. I had won with a flush, a straight and even a straight flush before that point and that is what almost convinced him to lay down a great hand. My neighbor went all-in with pocket eights and I ended up beating him with pocket nines! All that winning made them believe I was holding better cards all the time. Almost enough to surrender a pair of Kings!
Of course, the poker championship events we see on TV tell a story of lots of people folding good hands to a losing hand that was bluffed well. But we do not see all the times when those bluffing people pulled off extreme upsets against other players and the aura and the experience made the other players stop and think. Is this going to be a big mistake if I raise a hand I am not sure of?
So I would argue that bluffing is better left until you have won some hands, some lucky hands is better, and then use that personal aura and momentum to help you in a pinch when you need that little extra assistance. But don't mistake it for good cards It is no substitute.
Poker is an art and a science. Bluffing is part of the art. And the virtue of any art is that a master artist knows when to use it skillfully and when not to.
Bluffing takes skill and it takes some luck. In fact, I would argue bluffing only works in one case. When you are winning. You may get lucky by position when you bet on a hand and you are hoping for a card and someone mistakes your bet for a good hand already. Or if the other players have shown their weakness by checking, and then you raise you may fool beginners and you may scare off experienced players.
But I have found bluffing only works, in general, when you have been winning and the other players are scared that you have got them again. I can remember a time when I had a pair of fours, hole cards, and I was running up the bets on a table. I made most of them quit - except the eventual winner that had two Kings - because I had won some monster pots before that. I almost made him give up two kings because I had beaten them all in recent history with some lucky hands. I had won with a flush, a straight and even a straight flush before that point and that is what almost convinced him to lay down a great hand. My neighbor went all-in with pocket eights and I ended up beating him with pocket nines! All that winning made them believe I was holding better cards all the time. Almost enough to surrender a pair of Kings!
Of course, the poker championship events we see on TV tell a story of lots of people folding good hands to a losing hand that was bluffed well. But we do not see all the times when those bluffing people pulled off extreme upsets against other players and the aura and the experience made the other players stop and think. Is this going to be a big mistake if I raise a hand I am not sure of?
So I would argue that bluffing is better left until you have won some hands, some lucky hands is better, and then use that personal aura and momentum to help you in a pinch when you need that little extra assistance. But don't mistake it for good cards It is no substitute.
Poker is an art and a science. Bluffing is part of the art. And the virtue of any art is that a master artist knows when to use it skillfully and when not to.
Monday, April 19, 2010
Poker Tactics - The odds are conditional on sequential events
Most people get the probability of a straight or a flush wrong because they consider the act of determining the 7 cards up as a single event. This is an assumption made by a lot of people, and it is wrong. Most people, heard it from a guy who knows a guy who plays in Vegas and he says it is rare. Well that guy who plays in Vegas is wrong.
The fact is, if you count up the 5 cards you need for a straight or flush and divide it by the total deck size, then you are assuming that it all happens in one event. That is not the correct way to analyse it.
The true probability requires you to add the consecutive probabilities of several events together. When the exact event could happen on multiple attempts ( like getting the right cards on the turn, and the river ) then you need to add the probabilities together. That is a mathematical fact.
All these events are mutually exclusive because the cards can only occupy seven slots. Either you get the Ace of spades in your hand or you get a two of diamonds. If that is so, then you need to consider that the probabilities of all cards adds to one after each event.
The error people make is that they don't account for the sequential events.
If you want to know how likely two mutually exclusive and yet coincident events A and B are at the same time it looks like this: P(A and B) = P (A) * P(B). But if we have different events, one that occurs after the first one, then the probability is different. If we have two possible favourable events that don't occur at the same time, A and then B, then that probability is added, not multiplied. P(A or B) = P(A) + P(B). First A happens and then B could happen.
For example, you want to know what is the probability of a second Ace on the flop when you have one in your hand then the total probability is computed for the SINGLE EVENT P(Ace in flop). Assuming no one else gets an ace for 9 players and an ace isn't burned then the flop is one event then
P(Ace in flop) = 3/34 = 0.088235294.
But if you want to know what the odds are and you have several events consecutive then you need to compute the odds of each event and add them.
Let's say you have an Ace in your hand and none show up in the flop, then you have the turn and the river events to pick up that ace. Assume you have an ace, you are playing 8 other people, assume that the aces stay in the deck and aren't burned, and there are 3 remaining in the deck after the flop.
P(Ace) = P(Ace on turn) + P(Ace on river) = 3/30 + 3/28 = 0.1 + 0.107142857 = 0.207142857 or about 20% chance. You have at most a 20% chance of getting that Ace pair best case scenario.
You might get triple aces, one on the turn and one the river, but that is a little harder P(AAA) = P(Ace on turn) + P(Ace on river) = 3/30 + 2/28 = 0.1 + 0.071428571 = 0.171428571.
The odds of flushes and straights are very low when you consider the entire chances for one hand and the flop. But when you play with nine people, there are nine chances you will to get two straight cards (the start of a straight) or flush ( two of the suit) with your hand or in the other 8 hands at the table. Consider the odds at that point with 52 cards
2 2 2 2 2 2 2 2 2 18
-- + -- + -- + -- + -- + -- + -- + -- + -- = ---
52 52 52 52 52 52 52 52 52 52
= 0.346153846
People think that straights and flushes are low probability, but those combinations occur about one in three hands. That's quite a lot.
Most people calculate assuming 52 cards in all for this chance of a straight or flush, but it's only convenient for the first deal. It is a wrong approximation. The card count changes and therefore the probability changes as cards are removed. The trick is that as the card count reduces, the probability of one cards goes up. Sounds odd, but let's continue. Let's calculate the best case scenario for a flush.
Then you bet on those before the flop. The Flop is a separate event.
So you got your two cards and now there are 16 other cards removed. Let's say you have two hearts, Ace of hearts and 2 of hearts. You have 2 of 13 possible hearts. You want 5 of them. Of course some of them will go into other hands. If you make the assumption that hearts are 25% of the cards and there are 16 cards out there, then perhaps on average 4 cards dealt out are hearts in other people hands. The worst case is those cards are together in other hands. But since you have the Ace, and you are risking a flush, then you feel confident you have the best one out there. Of course, if the flop comes up 3 low clubs, you are going to run for the door and fold you hand. But let's say you want to know how good your flush chances are before the flop. Let's assume that the 4 hearts are in other hands. That leaves 7 more hearts. Essentially half of them are still available before the flop assuming random distribution and hearts are 25% of the deck. There will be times when there are no hearts left and there will be times when all hearts are left. But since you can't peak under other peoples hands, they frown on that I know, you need to make some reasoned assumptions.
Now there are 52 - 18 = 34 cards left in the deck. This is the new denominator for all probability. There are 34 cards remaining and you need the 3 of them to be hearts. There are 7 left outstanding. Let's say two hearts do come up on the flop, the eight and nine of hearts. Then 4 cards were used for the flop but the probability was
7
-- = 0.205882353
34
There might have been a heart as the burn card, but since the hearts occupy only 25% of the total cards that will happen on average 1 in 4 times. Let's assume that isn't the case. There are now 5 hearts left for the turn and the river.
There are now 30 cards remaining for the turn card. This is the new denominator for all probability. The turn takes 2 cards and you need one heart and it doesn't matter which. Again, there might have been a heart as the burn card, but since the hearts occupy only 25% of the total cards that will happen on average 1 in 4 times. Let's assume that isn't the case again.
Your probability of getting a heart is now
5
__ = 0.166666667
30
There are now 28 cards remaining for the river card. This is the new denominator for all probability. The river takes 2 cards and you need one heart and it doesn't matter which. Again, there might have been a heart as the burn card, but since the hearts occupy only 25% of the total cards that will happen on average 1 in 4 times. Let's assume that isn't the case again.
If you didn't get a heart on the turn, then you have one more chance at it. Assuming there are still 5 left your probability of getting a heart is now
5
-- = 0.178571429
28
So your total chances, with four hearts after the flop, are
0.166666667 + 0.178571429 = 0.345238096
Compare the chance of getting a flush (when you have four suited cards after the flop) with getting a second ace on the turn or the river.
Chances of getting an Ace = 0.207142857
Chances of getting a Flush = 0.345238096
Of course, this is predicting random events, so there is no guarantee that you will get the right cards when you want them. But don't underestimate just how likely a flush is.
Straights are a little nicer because you have 4 suits to play with. If you have 78 and on the board is 56 after the flop, then for the turn and the river you need either a 4 or a 9 to complete the straight. That is 8 cards left to get a straight rather than 7 above for a flush.
8/30 + 8/28 = 0.266666667 + 0.285714286 = 0.552380953
All these odds calculated are the best case scenario, they will almost never happen this well. In fact, the probability drops away when you start taking the right cards out in burn cards and in other player's hands. But it is important to stress that these are all likely events and you must consider the sequential nature of events to get the right odds.
The fact is, if you count up the 5 cards you need for a straight or flush and divide it by the total deck size, then you are assuming that it all happens in one event. That is not the correct way to analyse it.
The true probability requires you to add the consecutive probabilities of several events together. When the exact event could happen on multiple attempts ( like getting the right cards on the turn, and the river ) then you need to add the probabilities together. That is a mathematical fact.
All these events are mutually exclusive because the cards can only occupy seven slots. Either you get the Ace of spades in your hand or you get a two of diamonds. If that is so, then you need to consider that the probabilities of all cards adds to one after each event.
The error people make is that they don't account for the sequential events.
If you want to know how likely two mutually exclusive and yet coincident events A and B are at the same time it looks like this: P(A and B) = P (A) * P(B). But if we have different events, one that occurs after the first one, then the probability is different. If we have two possible favourable events that don't occur at the same time, A and then B, then that probability is added, not multiplied. P(A or B) = P(A) + P(B). First A happens and then B could happen.
For example, you want to know what is the probability of a second Ace on the flop when you have one in your hand then the total probability is computed for the SINGLE EVENT P(Ace in flop). Assuming no one else gets an ace for 9 players and an ace isn't burned then the flop is one event then
P(Ace in flop) = 3/34 = 0.088235294.
But if you want to know what the odds are and you have several events consecutive then you need to compute the odds of each event and add them.
Let's say you have an Ace in your hand and none show up in the flop, then you have the turn and the river events to pick up that ace. Assume you have an ace, you are playing 8 other people, assume that the aces stay in the deck and aren't burned, and there are 3 remaining in the deck after the flop.
P(Ace) = P(Ace on turn) + P(Ace on river) = 3/30 + 3/28 = 0.1 + 0.107142857 = 0.207142857 or about 20% chance. You have at most a 20% chance of getting that Ace pair best case scenario.
You might get triple aces, one on the turn and one the river, but that is a little harder P(AAA) = P(Ace on turn) + P(Ace on river) = 3/30 + 2/28 = 0.1 + 0.071428571 = 0.171428571.
The odds of flushes and straights are very low when you consider the entire chances for one hand and the flop. But when you play with nine people, there are nine chances you will to get two straight cards (the start of a straight) or flush ( two of the suit) with your hand or in the other 8 hands at the table. Consider the odds at that point with 52 cards
2 2 2 2 2 2 2 2 2 18
-- + -- + -- + -- + -- + -- + -- + -- + -- = ---
52 52 52 52 52 52 52 52 52 52
= 0.346153846
People think that straights and flushes are low probability, but those combinations occur about one in three hands. That's quite a lot.
Most people calculate assuming 52 cards in all for this chance of a straight or flush, but it's only convenient for the first deal. It is a wrong approximation. The card count changes and therefore the probability changes as cards are removed. The trick is that as the card count reduces, the probability of one cards goes up. Sounds odd, but let's continue. Let's calculate the best case scenario for a flush.
Then you bet on those before the flop. The Flop is a separate event.
So you got your two cards and now there are 16 other cards removed. Let's say you have two hearts, Ace of hearts and 2 of hearts. You have 2 of 13 possible hearts. You want 5 of them. Of course some of them will go into other hands. If you make the assumption that hearts are 25% of the cards and there are 16 cards out there, then perhaps on average 4 cards dealt out are hearts in other people hands. The worst case is those cards are together in other hands. But since you have the Ace, and you are risking a flush, then you feel confident you have the best one out there. Of course, if the flop comes up 3 low clubs, you are going to run for the door and fold you hand. But let's say you want to know how good your flush chances are before the flop. Let's assume that the 4 hearts are in other hands. That leaves 7 more hearts. Essentially half of them are still available before the flop assuming random distribution and hearts are 25% of the deck. There will be times when there are no hearts left and there will be times when all hearts are left. But since you can't peak under other peoples hands, they frown on that I know, you need to make some reasoned assumptions.
Now there are 52 - 18 = 34 cards left in the deck. This is the new denominator for all probability. There are 34 cards remaining and you need the 3 of them to be hearts. There are 7 left outstanding. Let's say two hearts do come up on the flop, the eight and nine of hearts. Then 4 cards were used for the flop but the probability was
7
-- = 0.205882353
34
There might have been a heart as the burn card, but since the hearts occupy only 25% of the total cards that will happen on average 1 in 4 times. Let's assume that isn't the case. There are now 5 hearts left for the turn and the river.
There are now 30 cards remaining for the turn card. This is the new denominator for all probability. The turn takes 2 cards and you need one heart and it doesn't matter which. Again, there might have been a heart as the burn card, but since the hearts occupy only 25% of the total cards that will happen on average 1 in 4 times. Let's assume that isn't the case again.
Your probability of getting a heart is now
5
__ = 0.166666667
30
There are now 28 cards remaining for the river card. This is the new denominator for all probability. The river takes 2 cards and you need one heart and it doesn't matter which. Again, there might have been a heart as the burn card, but since the hearts occupy only 25% of the total cards that will happen on average 1 in 4 times. Let's assume that isn't the case again.
If you didn't get a heart on the turn, then you have one more chance at it. Assuming there are still 5 left your probability of getting a heart is now
5
-- = 0.178571429
28
So your total chances, with four hearts after the flop, are
0.166666667 + 0.178571429 = 0.345238096
Compare the chance of getting a flush (when you have four suited cards after the flop) with getting a second ace on the turn or the river.
Chances of getting an Ace = 0.207142857
Chances of getting a Flush = 0.345238096
Of course, this is predicting random events, so there is no guarantee that you will get the right cards when you want them. But don't underestimate just how likely a flush is.
Straights are a little nicer because you have 4 suits to play with. If you have 78 and on the board is 56 after the flop, then for the turn and the river you need either a 4 or a 9 to complete the straight. That is 8 cards left to get a straight rather than 7 above for a flush.
8/30 + 8/28 = 0.266666667 + 0.285714286 = 0.552380953
All these odds calculated are the best case scenario, they will almost never happen this well. In fact, the probability drops away when you start taking the right cards out in burn cards and in other player's hands. But it is important to stress that these are all likely events and you must consider the sequential nature of events to get the right odds.
Sunday, April 18, 2010
Poker Tactics - Cards are King
The fundamental rule about Poker is this: it is governed by permutations and combinations of cards, and the better hands are governed by just how likely they are to occur. The highest hands, straight flush and four of a kind, are so rare that when they occur you will note them. They are rare because the mathematical odds of getting them in 7 cards ( Texas Hold'em two in the hand and 5 on the board ) are so rare.
This image to the left is the supremacy list of poker hands from the straight flush - all the same suit and in order - all the way down to the lowly One of a Kind where an Ace rules the world of bad hands.
The odds of a pair is 1098240 out of 2598960 or a little less than 50% of the time a pair will win the day. Aces are highest so Aces is a hand that most people play. The three luckiest hands are, AA, AK, and KK. So most people feel confident to play these hands. AK has a special place because if either a A or a K comes up then you have the high pair on the board. For those people who play the least risky, and therefore the most predictable, these are the main stable of play. For some of these players these are the only hands they will play.
When you play against people you don't know, and you are unsure of the tactics of when to bet and when not to, the most important factors to remember are the odds of a hand and the supremacy of the hands.
Bluffing won't turn away good cards. Position won't make a good player with a good hand worry. Good players wait for an hour to play good cards so they would be damned by the poker gods to let you take the pot if you try these tactics. The art of position and bluffing are important. But in the end, cards are kings.
Whenever you bet you must look at your odds of winning in the light of these two factors: can my hand beat most of the other possibilities with the cards on the table, and if not then can I get the cards I need to beat the others?
The deck of 52 cards is well known. The fact is that more players means more chances of seeing all those higher winning card hands. You need to be careful as you bet on a pair of aces that someone may have sneaked in two pairs of lowly sevens and nines. In the end two low pairs beat a pair no matter what the ranking.
Daniel Negreanu describes three levels of players. Level 1 players can figure out how good their own hand is. Level 2 can figure out what can beat what they have. And level 3 can figure out what the other player has. Before you can play well, you need to start with the basics and learn the order of cards and then learn to realize quickly how good your hand is and how to
Here is the fact about poker hands, you don't know how good yours is until you see the complete 7 cards. Until then, you are playing based on speculation, and betting and bluffing on how good you think your cards are. This game, the speculating and considering others cards, is done to cause tension on the players and make the excitement and disappointment real. Sometimes the long odds wins and sometimes the predicted hand winds. In the end, the odds favor the better cards. But what are better cards really depends on what people play.
In order to determine what are good cards, you need to consider just how you can win and lose.
There are five possible winning hands: high card, pairs (or sets), straights, flushes and straight flushes. Consider one of a kind as a special form of set and are ruled by the ace. Straight flushes are so rare that you can just consider them a form of straight. You may see a few in your lifetime, and probably not at time to win a monster pot. If you look at the compressed versions of the winning hands, that leaves really three ways to play for the best hand. Play to win with a straight, play to win with a flush, and play to win with a set.
The conservative form of play involves the sets, the harder form of play involves straights and flushes. Full house beats the straights and flushes so that is the best form of sets except four of a kind. When a full house is on the board, flush players and straight players beware.
Flushes and straights of five cards require some patience on the part of the player. A pair or two pairs only require four cards at most and therefore you don't need a complete five good cards. When you play a straight or flush however, you will need to wait for the turn or river to get that straight or flush sometimes. The best way to achieve these is playing suited connectors - cards in sequence and the same suit. The best way to play is to limp in betting and see if the cards come up on the flop. These cards make it even rarer to do well, so you may need to play more types of hands than this to survive.
Of course, since straights and flushes are rare combinations, this strategy is bound to cost you chips in the short term and make playing a lot harder to do. But the reality is that when you play against conservative players holding those good cards, aces and kings, you can defeat them easily and perhaps catch them trying to take too many chips in the process because when you play few hands you need to make a large amount of chips to make up for the lack of play.
The odds of a pair is 1098240 out of 2598960 or a little less than 50% of the time a pair will win the day. Aces are highest so Aces is a hand that most people play. The three luckiest hands are, AA, AK, and KK. So most people feel confident to play these hands. AK has a special place because if either a A or a K comes up then you have the high pair on the board. For those people who play the least risky, and therefore the most predictable, these are the main stable of play. For some of these players these are the only hands they will play.
When you play against people you don't know, and you are unsure of the tactics of when to bet and when not to, the most important factors to remember are the odds of a hand and the supremacy of the hands.
Bluffing won't turn away good cards. Position won't make a good player with a good hand worry. Good players wait for an hour to play good cards so they would be damned by the poker gods to let you take the pot if you try these tactics. The art of position and bluffing are important. But in the end, cards are kings.
Whenever you bet you must look at your odds of winning in the light of these two factors: can my hand beat most of the other possibilities with the cards on the table, and if not then can I get the cards I need to beat the others?
The deck of 52 cards is well known. The fact is that more players means more chances of seeing all those higher winning card hands. You need to be careful as you bet on a pair of aces that someone may have sneaked in two pairs of lowly sevens and nines. In the end two low pairs beat a pair no matter what the ranking.
Daniel Negreanu describes three levels of players. Level 1 players can figure out how good their own hand is. Level 2 can figure out what can beat what they have. And level 3 can figure out what the other player has. Before you can play well, you need to start with the basics and learn the order of cards and then learn to realize quickly how good your hand is and how to
Here is the fact about poker hands, you don't know how good yours is until you see the complete 7 cards. Until then, you are playing based on speculation, and betting and bluffing on how good you think your cards are. This game, the speculating and considering others cards, is done to cause tension on the players and make the excitement and disappointment real. Sometimes the long odds wins and sometimes the predicted hand winds. In the end, the odds favor the better cards. But what are better cards really depends on what people play.
In order to determine what are good cards, you need to consider just how you can win and lose.
There are five possible winning hands: high card, pairs (or sets), straights, flushes and straight flushes. Consider one of a kind as a special form of set and are ruled by the ace. Straight flushes are so rare that you can just consider them a form of straight. You may see a few in your lifetime, and probably not at time to win a monster pot. If you look at the compressed versions of the winning hands, that leaves really three ways to play for the best hand. Play to win with a straight, play to win with a flush, and play to win with a set.
The conservative form of play involves the sets, the harder form of play involves straights and flushes. Full house beats the straights and flushes so that is the best form of sets except four of a kind. When a full house is on the board, flush players and straight players beware.
Flushes and straights of five cards require some patience on the part of the player. A pair or two pairs only require four cards at most and therefore you don't need a complete five good cards. When you play a straight or flush however, you will need to wait for the turn or river to get that straight or flush sometimes. The best way to achieve these is playing suited connectors - cards in sequence and the same suit. The best way to play is to limp in betting and see if the cards come up on the flop. These cards make it even rarer to do well, so you may need to play more types of hands than this to survive.
Of course, since straights and flushes are rare combinations, this strategy is bound to cost you chips in the short term and make playing a lot harder to do. But the reality is that when you play against conservative players holding those good cards, aces and kings, you can defeat them easily and perhaps catch them trying to take too many chips in the process because when you play few hands you need to make a large amount of chips to make up for the lack of play.
Poker Tactics - Position is a Factor
Once a grizzled old farmer expounded to me, at the poker table, "Position is everything". He was trying to make a point about the position in the betting order can be a key factor in winning hands. And the way he played, it seemed like he relied on it. He liked to play very aggresively - raising before the flop and re-raising at will. It made for a hard time for the other farmers - they liked to play conservative for their Friday night poker game. These gents liked to play a slow game for the evening. They were unhappy with his constant bets and raises, they preferred to win or lose $10 in an hour and not $10 in a minute.
Position is a term used to refer to when you bet in relation to the big blind and small blind players. Sometimes position means that you get to see what the other players actions are before you get to make your move. Sometimes it helps in bluffing - when you are the last to bid and you can see everyone else call then it makes it easier to convince them that you may have the best hand. Sometimes you can bet first and even raise which may scare off players with medium cards waiting for a flop.
Poker is both an art and science. The science is in the probabilities and the statistics, and in the psychology of the other players. The art is when to apply it this knowledge to your poker game.
Position can be useful but it can also be a dangerous to your poker chip stack. Position is not a substitute for good cards. Just like bluffing can be over-used it is the same with position. It can be useful for some situations but use it at the wrong time and you will regret it.
I have learned from playing against the statistical players online that rarely do people - people that win at poker - stray from betting on good cards. They don't bet unless they can make something from the cards that they have in the hole. Perhaps they learned this the hard way, donating to other players until they learned their lessons, or perhaps they looked at the poker odds, read a few good books on poker, or just had a common sense approach.
If you are going to run against good players, and if they play a lot that is going to be true, then you need to understand that good cards are the foundation and the rest is just window dressing.
Position can help you when you need to convince others that you have a good hand but you don't when you are bluffing. You look like you have just check-raised everyone and since they will assume you are a good player so then it fits.
Position helps when you don't have a good hand before the flop and you want to scare people off. If you make a big first bet, then when the other good players see that they may leave before they see your cards. And then they may regret letting you have any easy win.
Position can help you when you have lasted in a game to the turn or the river and you are still not sure if you have the better hand. When you have an OK hand, say for example a middle strength pair and you are not sure if the other lasting players have aces etc, then position helps you if the other player has to bet first. He or she has to declare his intentions and you have the advantage. From then on in you get to see what the other person bets and you can use this either to trick them into betting more when you have the best hand or for you to bluff them after watching a check from them.
Position is a term used to refer to when you bet in relation to the big blind and small blind players. Sometimes position means that you get to see what the other players actions are before you get to make your move. Sometimes it helps in bluffing - when you are the last to bid and you can see everyone else call then it makes it easier to convince them that you may have the best hand. Sometimes you can bet first and even raise which may scare off players with medium cards waiting for a flop.
Poker is both an art and science. The science is in the probabilities and the statistics, and in the psychology of the other players. The art is when to apply it this knowledge to your poker game.
Position can be useful but it can also be a dangerous to your poker chip stack. Position is not a substitute for good cards. Just like bluffing can be over-used it is the same with position. It can be useful for some situations but use it at the wrong time and you will regret it.
I have learned from playing against the statistical players online that rarely do people - people that win at poker - stray from betting on good cards. They don't bet unless they can make something from the cards that they have in the hole. Perhaps they learned this the hard way, donating to other players until they learned their lessons, or perhaps they looked at the poker odds, read a few good books on poker, or just had a common sense approach.
If you are going to run against good players, and if they play a lot that is going to be true, then you need to understand that good cards are the foundation and the rest is just window dressing.
Position can help you when you need to convince others that you have a good hand but you don't when you are bluffing. You look like you have just check-raised everyone and since they will assume you are a good player so then it fits.
Position helps when you don't have a good hand before the flop and you want to scare people off. If you make a big first bet, then when the other good players see that they may leave before they see your cards. And then they may regret letting you have any easy win.
Position can help you when you have lasted in a game to the turn or the river and you are still not sure if you have the better hand. When you have an OK hand, say for example a middle strength pair and you are not sure if the other lasting players have aces etc, then position helps you if the other player has to bet first. He or she has to declare his intentions and you have the advantage. From then on in you get to see what the other person bets and you can use this either to trick them into betting more when you have the best hand or for you to bluff them after watching a check from them.
Monday, April 12, 2010
Poker Tactics - War is Deception
Sun Tzu had a powerful description of war:
War is deception
I think most people like poker because it's a little like a war - a psychological war. And there's money and risk involved - perhaps even girls will like you. War is hell. Poker is fun.
There is a lot of art in both war and poker. Sometimes it is won by the sneak attack and not the best weapons or stoutest warriors. Sometimes it is luck that breaks the tie. Predictability in either war or poker can be a fatal weakness.
I think that the best poker players understand this. They try to conceal their intentions and above all conceal their card strength. The best players don't just play one strategy. They vary play according to what the other guys think. Then they vary it again to take advantage of what other people assume about how they are playing. They change their betting value, when to bet, and how to act.
So if you want to win more hands, be unpredictable to a certain degree.
War is deception
I think most people like poker because it's a little like a war - a psychological war. And there's money and risk involved - perhaps even girls will like you. War is hell. Poker is fun.
There is a lot of art in both war and poker. Sometimes it is won by the sneak attack and not the best weapons or stoutest warriors. Sometimes it is luck that breaks the tie. Predictability in either war or poker can be a fatal weakness.
I think that the best poker players understand this. They try to conceal their intentions and above all conceal their card strength. The best players don't just play one strategy. They vary play according to what the other guys think. Then they vary it again to take advantage of what other people assume about how they are playing. They change their betting value, when to bet, and how to act.
So if you want to win more hands, be unpredictable to a certain degree.
Sunday, April 11, 2010
The Tactics of Mantracker Part 6
Here is the first in my series of recommendations on how to beat mantracker. The Mantracker game between horsemen versus runners is simple: the runners need to most everything right or the mantracker will catch you.
Here is some advice that will help the prey:
Here is some advice that will help the prey:
- Make a copy map Bring a permanent marker out to the competition and copy the map to both preys' forearms. By having a permanent map you won't lose it and when separated you can still navigate.
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