Hello,

I am looking to build my own little hand vs. hand trainer from preflop to turn but in order to build that I need the mathematical formula that will display the percentage hand vs hand.

For example, I want to have two hole cards displayed vs two other hole cards displayed and would like to know the equity in % depending on which street I choose, preflop flop or turn (with random board textures if it is postflop).

Since I suck at math, could anyone explain it or let me know the math behind it? Posting just the formula would be the best solution to my problem.

There isn’t a formula, you simply have to run out the possible boards to determine the %s.

There are ways to estimate but that doesn’t seem like what you want here.

You are basically looking for something that does what twodimes does.

To echo what David said, there is no magic "formula" for poker equities. You can see that by simply considering Hand A vs Hand B with only the River to come.

Suppose of the 44 possible river cards Player A will win A runouts, Player B will win B runouts, and T runouts will be a chop (a tie). Then Player A's equity will be (A/44) + 0.5*(T/44).

Of course, the hard part is determining A, B, and T. No "formula" can give you those numbers. Poker doesn't really work that way. You simply have to figure that out. Maybe Player A will win if the river is a Heart or a Ten, but not the Ten of Spades, etc.

And that is the simple case of only one card (the river) to come. Pre-flop or on any other street the determination of winning runouts is more "complicated". Tallying the winning runouts for each player (and the chops) is typically done via computer programs.

I am confident that poker equity websites have pre-computed all of the pre-flop two-player equities and simply then do a lookup to display them in any particular instance a user is interested in. I imagine that pre-computing extends to multiple players or other streets but I don't know to what extent.

Interesting answers, thank you!

I've always wondered how a program like Equilab exists where you put in hand vs hand on a flop and it gives you a % result even with two numbers after the coma, i.e. 35,63%.

The last paragraph what whosnext said seems to make most sense.

I think it's all simulation, not formulae.

you might be able to come up with something for 30 common situations or something like that. that's it's still simulation but not open-ended.