How to calculate percentages of poker hands when the program knows all hands?

Question

I am looking to calculate the percentages that you see on tv when watching poker in my java program. The difference between this question and many others, if unclear, is that the program DOES know all players hands and can therefore determine an accurate percentage. There are many websites such as this one: https://www.pokerlistings.com/online-poker-odds-calculator where you can input the players cards and it will give you the percentages. I was wondering if there were any all ready set algorithms for this or any java API that i could use in my program. I understand that my question may be a bit unrealistic. So if there is no algorithms or APIs, perhaps someone knows how it is calculated, so that i can try to construct my own algorithm?

In case there is still confusion: If there are 3 players and their hands are

player 1: As kh

player 2: 2d 3c

player 3: AH AD

I would like to know the percentage that each player has to win preflop, pre-turn and pre-river Thanks in advance.

Answer 1

The numbers are much smaller than you might expect, so brute-forcing is quite possible. The trick is to disregard the order the cards come out as much as possible. For example, if you're considering preflop probabilities, you only care about the entire board by the river, and not the specific flop, turn and river.

Given 3 hands (6 cards), there's 46 cards remaining in the deck. That means there's choose(46, 5) = 1,370,754 different boards by the river. Enumerate all boards, and count how many times each hand wins on the river. (Or more accurately, compute the equity for each hand, since sometimes 2 or 3 hands will tie on the river). This gives you preflop probabilities, and this is the most expensive thing to compute.

Given the flop, there's only choose(43, 2) = 903 boards possible by the end, so the flop probabilities (which you call the pre-turn), it's very cheap to enumerate all the runouts and compute the average equity for the three hands.

Given the flop and turn, there's only 42 possible river cards. So on the turn (pre-river), it's even cheaper to compute the hand equities.

You'll ideally need a fast hand evaluator, but that should be easy to find online if you don't want to write it yourself.

Answer 2

its inefficient, but you can loop through all of the cards left to be played and see how many each player wins in each scenario. Various speed ups can be made by eliminating possibilities ( IE no flushes if suits havent lined up )