Poker and Expected Value
Ed Miller, David Sklansky and Mason Malmuth, in their extraordinary book Small Stakes Hold 'em argue that poker is gambling but it is gambling in the same sense that brick and mortar casinos gamble. Assuming an even game, where everyone playing receives a random distribution of possible hands, one earns money by playing soundly and respecting expectation, or the money one expects to win or lose by making a single wager. The brick and mortar casinos make nothing but money because they take advantage of expectation. Winning poker players learn to make the most of the expected value (EV) of any given poker hand.
Let's take the game of roulette. On an American roulette wheel there are 38 numbers, 18 red, 18 black and 2 green numbers. The odds of hitting any number on a roulette wheel are 38 to 1 against or once every thirty-eight spins of the wheel. The casino pays out based on 36 to 1, reserving two numbers (the 0 and 00) as their EV. So what is the EV one can expect from a $5.00 bet on 23 Red? The specific number, 23 Red, will hit 1/38 times (2.63%) and will miss 37/38 times (97.37%). These are the only two possible outcomes as it makes no difference which number hits if it is not 23 Red.
EV=(%w)($won)+(%l)($lost) where %w is the percent of the time you win and %l is the percentage of the time you lose
EV=(1/38)(180)+(37/38)(-5)=(.0263)(180)+(.9737)(-5)=4.37+(-4.87)=$-0.50
In short, for every $5 bet you make on a specific number on a roulette wheel your EV for that bet is a loss of 50 cents. Each time your number hits the house pays you $5x$36 or $180 and each time your number fails to hit you lose your entire bet of $5. The house's EV looks something like it is not what you might expect!
EV=(.9737)(5)+(.0263)(-180)=(4.87)+(-4.73)=$0.14
That's right, the casino will earn $0.14 on your $5 bet. Not on each bet mind you but over time given an even distribution your EV is a small loss while the casino earns a gain even larger than your initial bet.
The roulette wheel is a rather simple analysis, there are only two outcomes, you win or you lose. Your information is known absolutely based on the probabilities that come from only 38 possible outcomes. Poker is not so simple. Information is always incomplete and the possibilities are quite large. On the other hand, when one grasps the potential outcomes based on a range of hands one is willing to play one increases the potential for generating positive EV.
Some hands, like AA or KK or QQ have positive EV from the outset. AA wins 85% of the time against a single random hand for example. Other hands, say 72 off-suit only wins 32% of the time giving the hand a negative EV. While this might not need saying, it makes sense to play AA in any position and to muck 72 off-suit from any position.
Poker is gambling when one chooses not to raise pre-flop in order to wait to see what the flop brings for this action reduces the EV for your premium hands. Entering too many pots with marginal hands is another way to reduce your EV because you play too many opening hands with negative EV. Remember the casino's goal to maximize EV by offering solid, fair games. Your goal as a poker player is to maximize your EV.
This is not to say that luck does not enter the picture. It does. Many years ago while playing roulette I hit 23 Red 3 times in a row. That happened once in my lifetime and never again. That was a lucky moment in time when the roulette gods happened to smile upon me. Nevertheless, over time, the distribution of hits to that number will be exactly 1 in 38 spins of the wheel.
I have had AA cracked and I have won with 72 off but I know that over time I will win 85% of the time I hold AA and lose 68% of the time I hold 72 off. Knowing this basic fact alone makes me better able to make positive EV hand choices pre-flop.
Ed Miller, David Sklansky and Mason Malmuth, in their extraordinary book Small Stakes Hold 'em argue that poker is gambling but it is gambling in the same sense that brick and mortar casinos gamble. Assuming an even game, where everyone playing receives a random distribution of possible hands, one earns money by playing soundly and respecting expectation, or the money one expects to win or lose by making a single wager. The brick and mortar casinos make nothing but money because they take advantage of expectation. Winning poker players learn to make the most of the expected value (EV) of any given poker hand.
Let's take the game of roulette. On an American roulette wheel there are 38 numbers, 18 red, 18 black and 2 green numbers. The odds of hitting any number on a roulette wheel are 38 to 1 against or once every thirty-eight spins of the wheel. The casino pays out based on 36 to 1, reserving two numbers (the 0 and 00) as their EV. So what is the EV one can expect from a $5.00 bet on 23 Red? The specific number, 23 Red, will hit 1/38 times (2.63%) and will miss 37/38 times (97.37%). These are the only two possible outcomes as it makes no difference which number hits if it is not 23 Red.
EV=(%w)($won)+(%l)($lost) where %w is the percent of the time you win and %l is the percentage of the time you lose
EV=(1/38)(180)+(37/38)(-5)=(.0263)(180)+(.9737)(-5)=4.37+(-4.87)=$-0.50
In short, for every $5 bet you make on a specific number on a roulette wheel your EV for that bet is a loss of 50 cents. Each time your number hits the house pays you $5x$36 or $180 and each time your number fails to hit you lose your entire bet of $5. The house's EV looks something like it is not what you might expect!
EV=(.9737)(5)+(.0263)(-180)=(4.87)+(-4.73)=$0.14
That's right, the casino will earn $0.14 on your $5 bet. Not on each bet mind you but over time given an even distribution your EV is a small loss while the casino earns a gain even larger than your initial bet.
The roulette wheel is a rather simple analysis, there are only two outcomes, you win or you lose. Your information is known absolutely based on the probabilities that come from only 38 possible outcomes. Poker is not so simple. Information is always incomplete and the possibilities are quite large. On the other hand, when one grasps the potential outcomes based on a range of hands one is willing to play one increases the potential for generating positive EV.
Some hands, like AA or KK or QQ have positive EV from the outset. AA wins 85% of the time against a single random hand for example. Other hands, say 72 off-suit only wins 32% of the time giving the hand a negative EV. While this might not need saying, it makes sense to play AA in any position and to muck 72 off-suit from any position.
Poker is gambling when one chooses not to raise pre-flop in order to wait to see what the flop brings for this action reduces the EV for your premium hands. Entering too many pots with marginal hands is another way to reduce your EV because you play too many opening hands with negative EV. Remember the casino's goal to maximize EV by offering solid, fair games. Your goal as a poker player is to maximize your EV.
This is not to say that luck does not enter the picture. It does. Many years ago while playing roulette I hit 23 Red 3 times in a row. That happened once in my lifetime and never again. That was a lucky moment in time when the roulette gods happened to smile upon me. Nevertheless, over time, the distribution of hits to that number will be exactly 1 in 38 spins of the wheel.
I have had AA cracked and I have won with 72 off but I know that over time I will win 85% of the time I hold AA and lose 68% of the time I hold 72 off. Knowing this basic fact alone makes me better able to make positive EV hand choices pre-flop.
