Full formula - equity

Hello FrakTool,

I recommend reading the articles:
Ranges & Equity (1): Introduction to Ranges
Ranges & Equity (2): Combos & Card Removal
Ranges & Equity (3): Equity Introduction
Ranges & Equity (4): Equity: Final Calls

If you have more questions don't hesitate to ask them.

Cheers,
SDK1987

the links dont provite the step to calculate based on exaustion or monte carlo.
i want the full explanation to equity.

It's too cumbersome to answer your question in the opening post. The video in (3) explained it pretty good.

The difference between Exhaustion and MC are:

• in Exhaustion you sum up all possible outcomes
• in MC you randomly pick a big number (10000, 100000) of outcomes from every possible outcome as a simulation

The second problem is not the "study of math", that's simple, it's more the "crafting of math" and summing up the result.
First you need three set P1, P2, B1 where P1 contains the hands of player1, P2 player2 and B the board.

P1 = {AsKs, QsKs}
P2 = {KsKd, KsKc, KsKh, KdKh, KdKc, KhKc}
B1 = {AsAdAhAcKs ,AsAdAhAcKs ... 3h3c2s2d2h2c}

f(P1​,P2​,B1​)

Equity = (∑ f(P1​,P2​,B1​)) / (2*N)

Then you count all possible outcomes and multiply that by two.
If player1 wins you add 2 if they tie 1 and lose 0.
Then divide result by the outcome and you have the equity.