While you will not win every single time you take this bet, you will have a better than 50% chance to double your money. So, for this bet, you have a positive expected value.
But just how much of an expected value do you have? Well, on a bet of $100, with a 51% chance to win, you will make, on average, $1.00 every time this bet is made. Sometimes you will lose $100, and sometimes you will make $100, but your average profit per play will be $1.00.
So, if your expected value on a fair bet was 60%, if you bet $100, you can expect to make $10.00 per bet, on average, for a positive expected value.
Now, what about a negative expected value? Well, obviously, if you bet $100.00, but only have a 49% chance to win the bet, over the long run, you will lose $1.00 per bet. This has a negative expected value of 1%. You will lose 1% of your bet, on average, each time you make this bet.
And of course, an expected value of 50% will neither win nor lose over the long run, so it is considered a neutral expected value.
So, the secret to making money is to make, and take, bets that have a positive expected value, and to not take bets with a negative expected value.
So lets apply this to poker.
Lets say you have Ac 9c on a board of 8c 7c 4h
You are last to act in the hand, and the pot is $50. The first player to act bets $5 into the pot. Everyone else folds to you.
For this example, lets assume your opponent has top two pair, 8h 7s
Knowing this, you need to hit your flush to win. So, what is your expected value for calling the $5.00 bet.
Well, first we need to know how many outs we have. To the flush, we have 9...the 9 clubs remaining in the deck. No other card can help us win. So, we figure with 9 outs, we have about a 19% chance of hitting a spade.
So, 19% of the money currently in the pot is ours. So, we figure out how much money is currently in the pot. $50 in, +$5 bet = $55.00
19% of $55 = $10.45
Our equity of the pot is $10.45. If we were to call such a bet, with such a hand, in a pot of this size, we will win on average $10.45
Because we will win on average $10.45, and we only need to call $5.00 to see if we win, we have a very nice positive E.V. (expected value)
Now, lets take that same hand again,
Ac 9c, on a 8c 7c 4h board, and the same pot of $50.00.
But lets assume your opponent bets $20.00 on the turn, and everyone folds to you. Is it worth a call now?
Well, lets see, there is $50 in the pot, plus $20 more of the bet, totaling a possible win of $70.00
You will still win 19% of the time, so what is the new expected value to call? $70 x 19% = $13.30
So, over the long run, if you call this $20.00 bet, you will only win $13.30 back. So you will end up losing $6.70 on average every time you call this bet.
In this case, you call has a negative expectancy.
The secret to winning at poker, or any gamble of any sort, is to take bets that have are a positive EV, and stay away from those that are a negative EV.
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