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I understand that pot odds is ratio between the pot amount and the call size. Stated differently it's the ratio Win amount : Lose Amount. In terms of Expected Value if the Win% of your hand is more than the pot odds then calling the bet will give you positive Expected Value.

Specifically pot odds would be this ratio (Pot amount + Opponent bet size) : (Your bet size)

This is assuming Win amount = Pot amount + Opponent bet size. However why don't we discount the money that the player contributed to the pot prior to calling the current bet (i.e. the blinds, any preflop bets, etc.).

This would mean Win amount = Pot amount + Opponent bet size - Our money already in the pot

and Lose amount = Your bet + Our money already in the pot. So adjusted pot odds would be:

(Pot amount + Opponent bet size - Our money already in the pot) : (Your bet + Our money already in the pot)

This gives drastically different pot odds depending on our prior contribution to the pot. Is there an explanation why people choose to ignore this? What am I missing here?

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    Why should it matter whether chips in the pot have come from your stack or not? At any point, you are playing for whatever is in the pot, regardless of whether the chips have come from your stack, villain's stack, or a house bonus, etc.
    – Andrew Chin
    Jan 29 at 10:07
  • Because pot odds relate to the Expected Value (EV) of a call. EV = Win% X Win amount - Lose% X Lose amount. EV is directly related to how you define your Win amount and Lose amount. If you include the amount of chips in the pot that came from your stack then Win amount decreases and Lose amount increases by that specific amount. This will require Win% to be higher for the call to be EV positive.
    – A. Alamo
    Jan 29 at 14:25
  • You can choose to use inaccurate definitions.
    – Andrew Chin
    Feb 2 at 16:57
  • Do let me know what the accurate definition for EV is.
    – A. Alamo
    Feb 4 at 0:21

3 Answers 3

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Once the money is in the pot it doesn't really matter if those chips used to be yours or not. Now they belong to the player that wins the hand. Think of these two situations (blinds are 1/2):

  • Everyone folds up to SB, SB raises to 6. BB calls. No more bets until the river and then SB bets 4. BB now has to call 4 to fight for a pot of 20 (so they should be winning at least 20% of the time for the call to be profitable)

  • UTG raises to 5, everyone folds up to SB, SB calls, BB folds. No more bets until the river and then UTG bets 4. Now SB has to call 4 to fight for a pot of 20 (so they should be winning at least 20% of the time for the call to be profitable).

These situations are different in many ways, but not in terms of pot odds or bet sizing on the flop. The amount of times you need to win for the call to be worth it is the same in both scenarios.

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  • In your 2 examples to make a profitable call on the river you argue win% should be at least 4:1 (this actually 20% not 25%). You are calculating the Expected Value (EV) of the river call to be EV = 20% X (12 + 4) - 80% X 4 = 0. So a player should be winning at least 20% of the time for the call to result in EV > 0. However the money in the original pot that came from player's stack does impact the EV. From the original pot of 12, 6 came from player's stack. Now EV = 20% X (12 + 4 - 6) - 80% X (4 + 6) = 2 - 8 = -6. If win% = 20% this is minus EV call. For the call to be profitable win% = 55%.
    – A. Alamo
    Jan 29 at 14:14
  • @A.Alamo You are right. I put the 25% as an edit after making the answer when in fact it was 20%. The bet is 4 but the pot will be 20, not 16. I'll edit the answer to correct for that Point still applies though.
    – David
    Jan 29 at 16:33
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Because there is a difference in a hand being +/- EV and each decision being +/- EV. Consider this: Two players each put 10 in a pot(20) until the river. P1 bets 10 on the river. P2 needs 1:3 (25%) to justify a call, because always folding leads to -10 (considering whole hand), and 25%win in showdown leads to -10 considering one hand, so that is the +/-0 EV point for that decision.

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Pot odds are a useful way of comparing how likely you are to win a hand to the relative payout you get if you do. Your prior decisions don't factor into either of those parts - the likelihood of winning the hand depends only on the cards and is entirely unrelated to betting, while the payout ratio depends only on what's currently in the pot and the current bet. Money in the pot isn't yours anymore, and chips don't "remember" anything - the fact that a chip used to be in your stack is meaningless.

It doesn't matter where the chips in the pot came from. Your past decision to put chips in the pot is finished, that should not inform your current strategy. If you did modify your pot odds strategy based on your past betting behavior, it would seem to imply that "your" chips in the pot are somehow more or less valuable than everybody else's. But that's not the case, whenever someone puts a $1 chip in the pot, the pot increases in value by $1, not by $0.80 or $1.20 depending on who put the chip in. It would be a little silly to suppose that in the case of a split pot, you would prefer to take your own chips back if you could identify them.

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