Yoshimiii said:
I think it would be helpful if you could go over it in more detail if you have the time. I sometimes calculate my pot odds wrong based on the number of streets to come and blockers and possible flush cards to come etc.
Okay, I'll go more in-depth. I have a bit of time at the moment where I literally have nothing to do, so this is prob good, haha.
Let's take a very simple example. We're HU on the river, facing a bet, and let's just say for simplicity that we'd end up all in (we don't have the option to raise, and therefore no FE). So we can call, hoping to win the pot, or we can fold. How do we know what our
expected value is for calling? It's called an EV equation. (Note that folding is ALWAYS zero EV.)
EV(call) = (Amount in the pot)x(% of the time we win) - (Amount we have to call)x(% of the time we lose)
Note that the amount in the pot includes the villain's bet. Also, the % of time we win is our
equity. In addition, when we call we can either win or lose, so (% of the time we win) + (% of the time we lose) = 1. So we'll re-write the equation more succinctly:
EV(call) = (Pot-size)x(Equity) - (Bet-size)(1 - Equity)
Now we assume that we want to make at LEAST a breakeven call, so EV > or = to 0. We know all the variables aside from Equity in this, so we do some algebra to solve for the Equity we need to make this true.
0 < (Pot)x(Equity) - (Bet)x(1 - Equity)
0 < (Pot)x(Equity) - (Bet) - (Bet)x(-Equity)
0 < (Pot + Bet)x(Equity) - (Bet)
Flipping things around and adding "Bet" to both sides:
(Pot + Bet)x(Equity) > (Bet)
Equity > (Bet)/(Pot+Bet)
This is the result I cited earlier. Note that we have said nothing about what the bet or pot sizes actually are. You just plug those in to determine the equity needed to make calling the bet +EV. So a very simple example:
The pot is $100, HU on the river in a $1/2 game, and we have $100 while waiting for our opponent to bet. Villain bets enough to put us all in, so an effective $100 bet. (IMPORTANT: The pot is now
$200.) What equity do we need against villain's range to make this a profitable call?
Equity > (Bet)/(Pot+Bet)
Equity > ($100)/($200 + $100)
Equity > 1/3 =
33.33%
So we need at least 33.33% equity against villain's range for this to be a breakeven call. Now let's look at how this relates to pot odds. We said there is $200 in the pot, and we are facing a $100 bet, which means are pot odds are $200:$100 or 2:1. So looking at these pot odds, we can go straight to our equation.
Equity > 1/(2+1)
Equity > 1/3 =
33.33%
It's just a short-cut that skips some of the details in spots where you would never want to do an EV equation and really don't need to. But note that all of this is a very straightforward and simplistic example. Things get more complicated if you have the option to raise, or if there are more players to act, and multi-street EV equations can get quite messy. But it doesn't mean this isn't important. If we can make a relatively accurate range for villain's on the river facing a bet like this, we can make a quick and mathematically sound decision on what is profitable.