Poker is a game of math, but not everybody thinks math is a game. Doug Hull set out to change that with Poker Work Book for Math Geeks, a “Sudoku book for poker” that presents the reader with a bevy of poker-specific mathematical exercises to flex their gray matter.

If you’re already geeked out on poker math, Doug’s book will be a blast. But if, like many players, you’re daunted by the complexity and challenge of doing math away from the table — let alone in real time during a game — he’s made this infographic to disavow you of any notion that poker math needs to be a burden. In fact, as you’ll see below, there are a number of handy shortcuts that Hull uses and has innovated upon to vastly simplify the math you need to do in your head before making a decision in a live game.

When it comes to poker math, winning players follow the “ABC” rule: Always Be Calculating. This infographic will give you the tools to start processing poker math at the table more quickly, intuitively and confidently.

### Check out Poker Work Book for Math Geeks now.

• Eileen Sutton

Doug hi, great stuff as always. What kind of situation would I be able to “expect to get the next two cards for calling a flop bet”? Thanks so much.

• Doug Hull

@Eileen,

Some situations I can think of:

You are looking for someone that is c-betting indiscriminately, then comes to realize the pot has gotten big on the turn.

If they are c-betting OOP, that is going to increase the chances of a free card.

If they have such a short stack that the turn shove bet is kind of like checking.

Historical inference

Tells based

• ron

Doug, what does the % equate to the max money I can call? thx

• Mark Baum

There are several mistakes in the percentages:
1. Aks vs 83 (not connected, not suited undercards) : 68% vs 32%
2. Ak vs 83s (not connected, suited): 65% vs 35%
3. AK vs 76s (suited connectors) 60% vs 40% (rounded up from 39.3%)

But,
4. JTs vs 76s (same suit): 66% – 34%
5. JTs vs 76o: 67% – 33%
6. JTo vs 76s : 63% – 37%
7. Jts vs 73o: 69%-31%
So, there’s a big difference between some of those cases and the chart would cause loss of money if pot odds are calculated, say by 60-40 as you show, when they are 70%-30.

Similar point below:

AKs vs A7s (dominated, same suit) – 70% – 30%
Aks vs A7o (suited vs off): 75% – 25%
AKo vs A7o (off, off): 73% – 27%
AKo vs A7s: 69% – 31%

In fact, even without calculating, one has to see that A7 vs AK cannot be better than K7 vs QQ. In both cases, the main percentage generator is when our key card (7 or K) hits, and the main percentage subtractor for us (if we are the weak hand) is when villain’s hand hits its key card (K for first case, and Q for second). However, in the second case, the chance of getting another Q when we get a K is lower than getting a K when we get a 7 (first case) because there are already two Q out, while only one K in the first case.
Therefore, the K7 vs QQ HAS to be better than A7 vs. Ak for the weaker hand. Not by a lot, but it cannot be worse!

I’m surprised! Those numbers ARE CRITICAL in the long run. Playing 70-30 is not the same as playing 60-40!

• Doug Hull

Mark,

These are estimates for the broad classes of these hands. Individuals will differ from the average. Rather than an exhaustive list of all possible match-ups, simple averages across all the hands that meet this classifications were used and rounded appropriately. The goal is a chart of eight situations that are easy to remember and are close enough. Within any classifications of 800,000 pre-flop match-ups into 8 categories, there will be approximations for simplicity.

• Mark

The goal and approach is good, definitely, but the percentages should be reasonably correct. A better way to present those percentages in the cases I mention is a range.