Poker Math and Poker Statistics
Due to a string of horrible beats lately I’ve decided to take some time off and run some math on various poker hands/outcomes instead of playing. I’ll be using Maple 8 and I’m sure most of the methods will be plagarized from various poker sources and put into one document, which I will call:
Jake’s Review of Poker Math
Last night I was doing some thinking and ran some simulations with Wilson’s holdem software and came up with some numbers that basically matched what I thought. This study has little scientific basis - randomized 1,000,000 hands to showdown with no betting. Later on I include some theory which no doubt creates a poorly devised experiment-theory hybrid.
So here is the first in the series:
| AK Details | A K Wins | 2 2 Wins | Split |
| Unsuited 0 Suit Matchup | 46.87% | 52.84% | 0.29% |
| Unsuited 1 Suit Matchup | 47.27% | 52.43% | 0.30% |
| Unsuited 2 Suit Matchup | 47.49% | 52.17% | 0.33% |
| Suited 0 Suit Matchup | 49.90% | 49.79% | 0.32% |
| Suited 1 Suit Matchup | 49.51% | 50.16% | 0.33% |
But really - to get a total average standoff percentage we need to realize that AK suited is much less likely than AK unsuited, or matching at least 1 suit between the two is more likely than not. So given that all cards have an equal chance of being dealt, we can write a few lists to discover the probabilities.
And Finally:
| AK Details | Prob. Occur | Y 2-2 | Y A-K | Y Split |
| U 0M | 0.1 | 5.28% | 4.69% | 0.03% |
| U 1M | 0.4 | 20.97% | 18.91% | 0.12% |
| U 2M | 0.1 | 5.22% | 4.75% | 0.03% |
| S 0M | 0.2 | 9.96% | 9.98% | 0.06% |
| S 1M | 0.2 | 10.03% | 9.90% | 0.07% |
| Totals | 1.0 | 51.46% | 48.22% | 0.31% |
So AK is a dog by 2.8% over 1,000,000 hands. Nothing really new there but interesting to see it evolve.
Just a few notes about split pots - these can only occur when a 5 cards appear on the board that beat both hands. So Straight, Some Full Houses, Straight Flush, Flush (Four of a kind is possible to split only when the overcard connectors do not contain an Ace). Of these, only the flushes depend on suit, and as the data indicates - as matching suits increase, so do the split pots (Albeit slightly, but due to more ‘other’ suited cards existing in the deck to give the non-matching flush).
Also consider that AK are the worst connecting overcards to have (by a slight amount) when going up against a low pocket, due mainly to straight possibilities. I’ll prove this to you in future posts, but if you think that you’re against low pockets - you’re better off playing J-10 and the like. However, if we showdown AK and J10 it would be quite apparent the good money was on big slick.
On to the next problem!