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Poker Math

Short-Stack Tournament Strategy in No Limit Hold ‘Em: Important Math Tips
By Mike H. of

We all know that the mathematics of probability plays a huge role in poker. Many of us, when thinking about great Texas Hold ‘Em mathematicians, conjure up images of famous poker professionals that include Andy Bloch, Phil Gordon, and Chris “Jesus” Ferguson. Although those three are renowned for their ability to calculate odds on the spot, there are plenty of helpful poker calculations that even a fourth grader can do with ease. Today I will discuss two calculations that almost every poker pro employs from time to time, mathematician or not.

The following math tips will be most useful if you are playing in an “all-in or fold” mode. You might be wondering why a solid poker player would ever use that strategy. Well, perhaps you are short stacked and battling the increasing blinds in a tournament, or perhaps you are playing a low stakes cash game against a drunk opponent that will call your all-in with virtually any two cards. I will show you two basic math formulas that will help you get all of your money in pre-flop with confidence, thus eliminating the need to make tough commitment decisions post-flop.


Definitions vary as to what being short-stacked entails among pros, but most agree that, with a stack that’s 7-10 times the big blind, your ability to simply “see a flop” is eliminated. In this situation, you must look to narrow the field pre-flop by risking your entire stack.

If you sit at a poker tournament table often enough, you will often hear what I like to call “the short-stacker’s lament” (which typically includes cries such as “just give me one ace” and “time to gamble”). However, being short-stacked is not a license to be wild. It is not a license to gamble. You must still take calculated risks in order to be successful.

Contrary to popular belief among beginners, any Ace-rag is not good enough to go all-in with, unless of course you are extremely low in chips (e.g. 3 big blinds left). There is a simple math tip that will help you figure out when to fold the A-8 and lower. Here it is, in 1easy step:

- Look at your kicker with the ace. Then count how many players still have to act behind you before the flop (including the small and big blind). If your kicker is lower than the number of players left to act (e.g. You have A-6 under with 8 players left to act), then there is a greater than 50% chance that you are dominated (meaning someone has a bigger Ace-X or a pocket pair that is 6’s or higher).

*Note: This approach is most useful when the action is folded around to you pre-flop. Obviously, if someone makes a big raise in front of you, you should still put them on a strong hand.

The second helpful math tip I can give you for short-stack situations will allow you to determine the chances of someone having a higher pocket pair than yours. (Again, as with the first math tip, this formula will only help you when action is folded around to you. You must still respect the raises of the people who act in front of you.) Here is the formula, in 3 steps:

1. Count the number of possible pocket pairs that are higher than yours.

2. Multiply that number by the number of players yet to act.

3. Divide that number by 2.

The result of that math will represent the approximate percentage that someone is holding a higher pair. Here’s an example:

You have pocket 5’s and are the first to act after the big blind. There are 9 people sitting at your table, including you. You have 10 big blinds left. What should you do?

1. There are 9 possible higher pairs than yours.

2. There are 8 people left to act after you.<,/p>

(9 x 8) / 2 = 36% chance that someone has a higher pocket pair.

The most important point that I am trying to make is this: there is a way to play smart poker while short-stacked. You do need a certain element of luck to get back into tournament contention, but taking calculated risks will help make it easier. There are proper times to fold pocket 2’s and A-7. Hopefully you will find this information helpful.

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