## August 25, 2020

### Pot odds

Pot odds is simply a term for the price you are getting laid by a bet. You can compare this to your assumed equity in the pot to make a judgement to continue or not. So

Pot odds = Bet amount / Total pot after the bet is called

If our equity is higher than the pot odds, we can call (assuming no further action possible, or at least that we realize our equity exactly). In the previous example, our equity was around 17%. If we assume our opponent is betting all-in on the turn here (and that our J high never beats his bluffs), we can calculate the maximum bet we can call directly from the above formula when the bet is X times the pot before the bet:

17% >= Bet / Total pot

or

17% >= (X*Pot before) / (Pot before*(2X + 1)

which can be written

17% >= X/(2X + 1)
=> X <= 0.25

In other words, with this equity, we can call the bet given the assumptions above if the bet is less than 25% of the pot.

The expression X / (2X + 1) can be used directly to compute a few pot odds that can be useful to know by heart. To call a bet of half pot, you need to be good 25% of the time, pot sized leads to 33% and twice the pot to 40%. As the bet gets larger and larger, the needed equity will approach 50% as most of the pot to win will be in the bet and less already in the pot.

You'll sometimes find pot odds expressed in ratios, like 3 : 1, but personally I find it easier to think about total pot and percentages directly, rather than going via ratios such as the one mentioned for a half pot sized bet.