Expectation Value (EV) Calculation (Page 1 of 4)
Any action you make in poker game should be focused on making a profit. Your efforts are worthwhile if they lead to the maximum profit possible or have the best average profit value. The average value of a possible profit is also named Expectation Value (EV).
Sometimes there are situations when you have several possible ways to play the hand. The profit of each variant = ev1, ev2,…,evN, the possibility of each variant = p1, p2,…, pN accordingly. Then the expectation value of the profit in the given situation is calculated by the formula:
EV = ev1*p1 + ev2*S2 + … + evN*SN (*)
The following is a very complicated example, but it has great practical value and touches on all the basic moments and rules of calculation. Let us assume that you have AK and raised on the preflop. The contender re-raised. Both stacks are 100BB. What is your best move? Should you call his re-raise, fold or re-raise (4bet)?
To answer these questions you need to calculate the EV of the call and the re-raise. The EV of the fold, obviously, is zero.
It is necessary to note that the EV of an action is the difference of our stack between the end and the beginning of an action, but not at the beginning of a hand. You cant get the money you have just invested in the pot.
When you call:
Let us set a task first:
The opponent made 3bet of your raise (raise=5??, 3bet=15??). You need to determine the possibility of your opponent having certain hands.
Let us divide the range of 3bet into two groups
The first group: he will play 3bet every time; these are QQ+ and ??.
The second group: he will play 3bet less than 100% of the time.
JJ: 70%. It means that he will re-raise with JJ 70% of the time, and will not make any further play.
AQ, ??: 30% (no more for small limits)
AJ, QK: 20%
1)?? and ?? have three combinations each, QQ-6, ??- 9, total 18
2)JJ – 6
3)AQ – 12, ?? – 6, total 18
4)AJ, KQ – 12 each, total 24
The total number of hands the opponent may re-raise with
13+6*0.7+18*0.3+24*0.2 = 32,4
The possibility the opponent has ??:
?(??) = 3/32.4 = 0.09.
The possibility of other hands:
?(??) = ?(??) = 0.09.
?(QQ) = 6/32.4 = 0.19
P(AK) = 9/32.4 = 0.28
P(JJ) = 0.7*6/32.4 = 0.13
P(AQ) = 12*0.3/32.4 = 0.11
P(TT) = 6*0.3/32.4 = 0.06
P(AJ) = P(KQ) = 12*0.2/32.4 = 0.07
Lets calculate the EV of various possibilities:
AA:
If you have K and/or A on the flop you should play with your entire stack.
The flop with a king and/or an ace may happen 23% of the time.
You may calculate this in the following way: one ace and three kings are left in the pack, four cards. To calculate the required probability, lets calculate the probability of the opposite situation – there will be neither an ace nor a king on flop.
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