Courtesy of Cyndi Papia
When trying to figure out their chances, most people do the counting in probabilities. Those rules are better known.
Sometimes you may just as well use the odds numbers straight off the shelf. Here are some simple rules for odds counting.
The +EV formula
This is a quick way of finding out whether you should call or fold.
We assume you have an idea of both your pot odds and your winning odds. (See also What Is Odds in Poker?)
Let's say you have winning odds of A-to-B and pot odds of C-to-D. For a call to be correct, the following "+EV formula" must hold:
AC - BD > 0
If this holds, your call is +EV.
Example: With a flush draw on the turn, let's assume your winning odds are around 1:4. After the opponent bets three quarters of the pot, your pot odds are 7:4. Is a call correct? (We'll ignore implied odds for now.)
According to the above, we have that A:B is 1:4 and C:D is 7:4. This gives us the following evaluation of the +EV formula:
AC - BD = 1*7 - 4*4 = -9
Which is below zero. In this case, calling cannot be motivated by the flush draw alone.
Example: You're on the river in the WSOP Main Event with the second nut straight. You bet $300,000 into a million dollar pot and an opponent puts you all in for your remaining $800,000. You tank for five minutes and conclude that the odds that he has you beaten are 3:5 (you're a 37% dog). Call or fold?
Your pot odds are 13:8, your winning odds 3:5, and the +EV formula becomes:
AC - BD = 13*3 - 8*5 = - 1
You have a fold, seen in pure "chip nomination EV". But it's a close call. The fold is marginal, and other factors that we have neglected here could tip the scale in favor of an all in call.
A picture says more than 1,000 words
Maybe this picture can visualize the +EV Formula. Or maybe not.
If the green rectangle is larger, you should call
Note: To use the +EV formula, you need to have the odds numbers in the right order:
A = your chance of winning
B = your chance of losing
C = the pot size
D = the required bet
The odds of "either or"
If there are two ways for you to win a hand, you're looking for the combined odds for the two events.
Say that you have winning odds of A:B for the first event and C:D for the second.
Then you have the following odds that at least one of them will occur:
( A*C + A*D + B*C ) : B*D
This little formula is really easy to use even in the middle of the action, which takes away the necessity of memorizing a lot of odds beforehand.
Example: You have a flush draw on the flop. You can win if a spade comes on the turn OR on the river. As a simplification, let's assume you have odds of 1:4 on both streets. Then the combined odds are:
1*1 + 1*4 + 4*1 : 4*4 = 9:16
Which is very close to the 1:2 odds you usually see listed for this situation.
Example: You flopped a set but need to improve to a full house to win. What are your chances?
You have seven winning cards on the turn and ten on the river (any card that pairs the board). You have odds of 7:40 OR 10:39. Let's simplify to 7:40 OR 10:40. The total odds are:
7*10 + 7*40 + 40*10 : 40*40 =
750 : 1600 = 7.5 : 16
Your winning odds are close to 1:2, corresponding to a 33% probability.
Of course, this calculation isn't as simple to pull off when you're facing an all in bet at the final table of the WSOP. But now you know the answer.
(This calculation also includes the case where your hand turns into quads. Which is okay, since it's even better.)
The odds of "both"
If you can win only if two separate events come true, such as two running sevens or two spades, the combined odds look like this:
A*C : ( A*D + B*C + B*D )
(Notice the similarity with the above formula, which makes them easy to memorize.)
Example: To make your runner-runner flush, you need a spade on the turn AND a spade on the river. Your combined odds are:
1*1 : 1*4 + 4*1 + 4*4 = 1 : 24
Odds of 1:24 mean a probability of 1/25 which is four percent - your chance of making a nice little suckout here.
/Charlie River
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