Poker and Expectation

Calculating Expectation:

The thought processes behind expectation can be quite complex, but thankfully the maths behind it is simple. For example, if you were offered a series of bets based on flipping a 2 sided coin where you make a $10 profit if you win and a $1 loss if you lose. Assuming there can only be two outcomes, each which has exactly a 50% chance of occuring, probability dictates that you will lose $1 half the time and gain $10 the other half.


Basic maths comes into play here:

(0.5 * -$1) = -$0.50 loss
(0.5 * +$10) = +$5.00 profit

In order to calculate the expectation of this play, we add the positive and negative scenarios together:

(-$0.50) + (+$5.00) = +$4.50

It is understood that if you take the coinflip bet, even though you will only ever either win $10 or lose $1, each flip has a value of $4.50 profit.

The grey area of expectation is that you must determine how likely an event is to occur, the more accurately you achive this, the more accurate your expectation calculations will be. Nobody can be certain that they're making the correct mathematical play every time, that's an unrealistic expectation of anyones poker skills, but thinking in terms of expected value will give you a guage on whether a certain play is profitable in the long term.

Making these calculations at the poker table are possible, but not very practical as they require plenty of thought, it's advisable to use expectation as a post analysis tool to help understand which bets are making you money and subsequently which plays should feature most prominently in your poker arsenal.

Don't forget, folding never has a positive expectation, you can only lose money by folding, especially in a game like Texas Hold'em which arguably favours the aggressor, but there are many situations that arise where a positive expectation is highly unlikely and the most profitable course of action is to give yourself the best chance of having the smallest negative expectation; win the most when you're expectation is likely to be positive and minimise your losses when you expect the play to lose you money in the long term.