A handy and simple implied odds formula

[ventrolloquist]

So I decided to figure out a formula for the minimum amount you need to win by the river if you want to make an unfavorable call and use implied odds instead of pot odds.

It's:

X = (Amount to Call / Hand equity) - Pot

Where X is the minimum amount you have to win on future streets to make a profitable call. And where pot is the size of the pot after you call an opponent's bet on the current street.

Here is how I got it. You just add X to the total pot size in the pot odds formula and isolate X.

Pot odds = Amt to call / ( opp bet + current pot size + amt to call)

Substitute "pot odds" with your hand equity to find the break even size for X, and add X to the denominator to get the total pot size after all betting is over after the river.

Hand Equity = Amt to Call / ( opp bet + current pot size + amt to call + X)

Then just combine all the stuff in the denominator into one simple variable called Pot which is the pot size after you call the bet.


Hand Equity = Amt to Call / ( Pot + X)
Pot + X = Amt to Call / Hand Equity
X = ( Amt to Call / Hand Equity ) - Pot

Hand equity can be determined however you want including using the rule of 4's and 2's and dividing that by 100 to get a decimal.