A simple pot odds example
We'll look at a simple situation. When the hand starts, you and your opponent both have $600 and when the turn card comes, you've both put $200 in the pot.
The pot is $400 and you both have $400 left.
If your opponent now bets his last $400, you can either call or fold. If you call, the pot odds are 2 to 1 - you bet 400 to win 800.
According to all the pot odds articles out here, you then need winning odds of 2 to 1 or better for the call to be correct. And winning odds of 2 to 1 translates to winning chances of 33%.
According to this theory, if you win one time out of three, you'll break even in the long run. If your winning chances are better than 33%, you'll show a profit.
The disbelieving question
But is this correct? Maybe you feel that some of the money in the pot was yours to start with, so how could it be counted as a win?! Shouldn't the money that you put in be ignored in this kind of calculations?
How could you win more than the $600 that your opponent had at the start of the hand?
Let's run a check on the pot odds formula by doing the full calculation.
Control calculation
In the above example, if you fold you'll have $400 left, which means that you've lost $200 in the hand.
If you call and lose, you'll have zero, you've lost $600. If you call and win you'll have $1200 which is a $600 win. Let's put it all together.
If you call with a probability p of winning, your expectation is:
E(call) = p*600 - (1-p)*600 = p*1200 - 600
Now we compare this to the expectation for folding. As we saw above, if you fold you'll always lose 200, so the expectation for folding is:
E(fold) = -200
What must your winning chances be for the two expectations to be equal? Put an equal sign between the two expectations and solve for p:
p*1200 - 600 = -200 =>
P*1200 = 400 =>
p = 400/1200 =>
p = 1/3
According to our calculation, calling is as good as folding if your winning chances are 1/3, or 33%.
This is the same result that was predicted by the ordinary pot odds theory. It seems to be good after all. That's probably why it's being used so much.
Are we clear?
If this is still confusing, it may help to look at it this way:
Once the money is in the pot, it's not yours anymore. If you want it back, you'll have to win it!
/Charlie River
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