Lesson: about odds

Okay, I've been thinking about it and this is probably the way conceptually to think about odds.

Say you are 3/1 to win a hand. What does that actually mean?

You are at point A, the action point. It's the point at which you must decide whether to bet, call or fold. Your odds at that point represent your chances of getting a certain outcome (the one favourable to you). All the figures we are bandying about express those chances.

So. You are at A, and after you decide, you will be at B. Say you take the odds.

It's as though there are four point Bs: B1, B2, B3, B4. Imagine this is a quantum universe (which it is), in which all possibilities happen (they probably do).

B1 is favourable for you.
B2, B3, B4 are not favourable for you.

3/1 says there are four outcomes, and one is good for you.

You can always think of odds in that way. Just sum the two sides and consider that you have that many outcomes. If your odds were 3/2, you have five outcomes, two favouring you.

Okay. So how does that fit in with a/ equity and b/ pot odds?

A. Equity


Your equity in this sense is the share your favourable outcomes have of all possible outcomes. When you are 3/1 to make your hand, you win it one out of four times.

You can figure out what your odds are as a percentage by simply doing this: divide 100 by the number of possible outcomes, then times that by the number of favourable outcomes.

I know that sounds complicated, but really it isn't. More importantly, you usually think of it the other way round.

We were talking about QQ vs AK. We say QQ has 56% equity versus AK.

So what are we saying? Well, equity always totals 100%. You can't win more than everything. And this is in any case how we describe probabilities: 56% just means 56 out of 100.

Out of 100 outcomes, if you hold QQ vs AK, there are 56 that are favourable. You can also write that as 0.56, which is handy when you're figuring out how much you stand to win or lose. (If you both have stacks of 1500, he shoves and turns over AK, and you are thinking about calling, you know that you stand to win 0.56 x 3000, and the amount you lose is always your bet. This just means that if you played the hand 100 times, you would expect to win 56 times and lose 44 times, which would average out to 0.56 x 3000.)

B. Pot odds

You can easily figure your pot odds. They are always (money in the pot) / (the bet you have to call).

If the pot is 100, some guy puts in 50, and you are asked whether you want to call, your pot odds are 100+50 / 50, which is 3/1. So when should you call?

You should call when your odds of winning are better than 3/1. How you can figure that out is for another day, but this is a key idea in poker.

3/1 means that out of four outcomes, one needs to be favourable to you. Remember our little formula? Sum the outcomes = 4. Divide that into 100 = 25. Times that by favourable outcomes - 25. You need to be a 25% chance against whatever he's betting with to win.

Luckily, there are tools to figure out whether you actually are that good a chance against his range, so long as you can make a reasonable estimate of what hands he can have. You can get by in STTs with a very sketchy and basic knowledge of pot odds. Basically, you need to know when you are good to push with a draw and when you are being offered such good odds that you should not fold. But you can learn both without having too good a grasp of the underlying concepts.

But this you do need to understand. Each set of outcomes makes a pie that totals 1. You are always going to end up with 1 or 0. But conceptually, before a play you can consider yourself to have a virtual slice of the pie. You will make a lot of decisions that depend on how big that slice is. And that pie is intimately connected with another (I know, way too many pies), which we will consider next. Just as you have equity in every hand (which is just the amount of outcomes that will favour you), you have equity in the tournament (which is the amount of the tournament's prizepool your chips are currently worth).

Conceptually, what matters is that you understand that even though you really end up with 1 or 0 -- or in prizes with 50/30/20 -- at any point, you have a virtual slice of the pie, which we can describe in percentages.