How can I calculate my total odds given different possible events?

Question

Let's suppose I have 25% probability of drawing the winning hand, equal to odds of 3:1. Let's also assume that I’ve tracked my opponents and calculate that there is a 50% chance they will fold to a bet or raise (if their loosing risk is too high), equal to odds of 1:1.

If I only consider my odds of improvement then I'll probably fall into a wrong betting decision where I'm not maximizing my winning neither make them actually fold. Then, given this two different probable events that computed together will tell my winning chances, how can I calculate the total odds?

Answer 1

You're not supposed to calculate the chances of you winning, that alone is irrelevant for us. It's okay to lose 99 times out of a 100 if you win 100 times what you lose when you do win, resulting in a break-even overall scenario. Each hand has different stacks, raise sizes and equity distributions.

You should be calculating how much equity you expect to win or lose by making a certain play. You do this by calculating how often a specific event occurs (villain folds, villain calls and wins, villain calls and loses) and your equity when that event occurs. The sum of all events give you an indicator of your expected value.

There are two events that can occur here really, villain folds or villain calls. This is when you're applying pressure, i.e. you're applying fold equity. If you're just calling then your equity is only the latter part of this formula because calling has no fold equity (there do exist rare live instances where this does happen though, i.e. villain mucks out of turn).

For the folding event you should estimate how often villain is folding, for example 70% (you do this by listing up villain's range and estimate how big portion of that range folds). When villain folds you win 100% of the pot so your expected value for this event is 70% * the pot.

For the latter part of the formula you take the event, which is 30% likely to take place in our instance, and multiply that with the following equation: (total amount won when villain calls and you win * your equity vs. villain's calling range) - (total amount lost when villain calls and villain wins * villain's equity vs. your raising range).

The sum of these two events is your total expected value when raising.

Jonathan Little explains this pretty well in his books but you can use his free equity calculator which explains what I just said in details. You can even try some examples.