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StrategyFixed Limit

Mathematics: Implied odds and Reverse Implied Odds


In this article
  • Implied odds take future winnings into account
  • Reverse implied odds take future losses into account
  • When can you give yourself which odds

The bronze section introduced you to the concepts of odds and outs, and pot odds. Pot odds, as you should already know, are the ratio between the amount you can win and the amount you have to invest to stay in the hand. A standard situation, which you would calculate pot odds:

  • You have a draw.
  • Your opponent bets.
  • You have to decide whether to call or fold

You can determine whether it is profitable to call or fold by calculating the pot odds. This, however, is only half of the story; the pot odds alone fail to take the possibility that more money will enter the pot into account.

A draw hand can often play out as follows:

  • You hit your draw and your opponent keeps betting or calls bets from your side. Or:
  • You hit your draw, and your opponent hits an even better hand and you pay him off.

Both of these possible scenarios have one thing in common: more money enters the pot on the later streets. The pot odds fail to reflect this, as they are defined by money that is currently in the pot. This is where the concepts of implied pot odds and reverse implied pot odds come into play.

What are implied pot odds?

You've probably already heard of the notion of implied pot odds (or implied odds) in a forum discussion or coaching. Implied odds are modified pot odds that reflect the possibility of more money entering the pot on later streets. You know your opponents won't fold every time a possible draw completes, which means that you can expect them to invest more money on later streets when you do complete your draw. Even if they don't continue to bet, you can probably get a call.


0.50/1.00 Fixed-Limit Hold'em (10 handed)

Pre-flop: Hero is BU with J, 9
2 folds, UTG+2 calls, 2 folds, MP3 calls, CO calls, Hero calls, SB calls, BB checks.

Flop: (6.00 SB) A, 8, 7 (5 players)
SB bets, BB folds, UTG+2 calls, MP3 folds, CO calls, Hero???.

Final Pot: 9.00 SB

There are 9 Small Bets in the pot, which means you have 9:1 pot odds. You need 11:1, however, to justify calling with a gutshot draw. You theoretically have to fold. Let's suppose you call in spite of the odds, and the turn shows...

Turn: (5.00 BB) T (1 players)
SB bets, ….

Final Pot: 11 SB

There were 9 Small Bets in the pot on the flop. There would theoretically have to be 2 more in the pot to justify your call. And that is exactly what happens on the turn. You hit your straight and the SB bets. Now that there is an additional Big Bet (2 Small Bets) in the pot, your call on the flop was correct.

You can assume that your opponent will invest another Big Bet given his action on the flop. Your possible winnings are therefore higher than the amount currently in the pot, since your opponent is certain to invest again on the turn (if he doesn't bet, he will certainly call). And there you have it, your implied odds.


Implied pot odds are modified pot odds that take possible winnings from future bets on the later streets into account.

Implied pot odds
= (current pot size + amount still likely to enter the pot : amount to call

To make one thing clear: your assumptions about possible bets by your opponents in the future streets are always speculative. You can be pretty sure sometimes that your opponent will call you down or fire at least one more barrel on the turn or the river, but nothing is ever certain.

The size of your implied odds depends on a multitude of factors, such as ...

  • … the strength of your opponent's hand.
  • … the number of opponents and their respective playing styles.
  • … how obvious your hand is to your opponents.
  • … your image.

An opponent with two pair will rarely lay down his hand when a gutshot draw completes. A maniac might even start a bluff on the card that completes your draw. And calling stations don't like folding, even when an obvious hand like a flush hits. And, in general, the more players involved in the hand, the more likely that one of them will have a reason to call.

You have to pay attention to all these things if you make correct assumptions about your implied odds. Before we can go into further detail, however, we have to take a look at the flip side of the coin: reverse implied odds.


That's not the entire article...

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