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This question is about calculating odds without knowing the opponents cards.

Calculating odds are an essential part of playing poker, and many online poker sites offer calculation services, such as this 888 poker service, which is probably powered by some kind of Monte-Carlo-Simulation.

Of course the odds are relative to the number of opponents at a table: Having AA preflop, gives you a ~85 % win against a single opponent, and a 31% win against 9 opponents.

My question is how to process opponents who has folded.

Example 1: (6 player table, preflop, you are BB): 4 players have folded. SB tries to steal your blind. You want to calculate your odds; Should you set opponents to 5 or 1 to get the most accurate estimation?

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  • It doesn't matter about the people who folded. You don't know their cards you assume they're still in the deck.
    – Grinch91 ♦
    Jan 5, 2018 at 14:01
  • I respectfully believe you are incorrect. As exemplified, the odds are heavily dependent on the amount of opponents. Having KK against 9 opponents makes it more likely to be outgunned by AA than having KK against 1 opponent.
    – Vingtoft
    Jan 5, 2018 at 14:07
  • Yes of course it increases the odds of any random two cards beating you, either by being better preflop or a random flop that smashes them. I think after re-reading your question I misunderstood your question initially. Is your question to know do you only factor the remaining players into calculations or the actual process of working out the percentage?
    – Grinch91 ♦
    Jan 5, 2018 at 14:13
  • That's exactly correct: My question is if I only factor the remaining players into calculations or if i should factor initial amount of players, or perhaps a third solution
    – Vingtoft
    Jan 5, 2018 at 14:16
  • Ok my apologises, brain fart on my end and misreading. So yes, you only factor the players remaining in the hand into your calculations, as the other hands are dead and not playing against you.
    – Grinch91 ♦
    Jan 5, 2018 at 14:17

2 Answers 2

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Grinch91 is correct.

The standard statistical approach is to treat every down card as an unknown card. A folded (mucked) hand is no different than a hand not dealt.

On a table of 6 if 4 fold you have one opponent.

Correct no one is likely to fold JJ+ or a big suited ace. This is called card removal. Address this statistically is complex and for the most part you just play poker.

Someone is not likely to bet with a random hand.

If there are 4 folds and I have ATs I like my hand better as not likely an ace is folded. If I have 78 suited I don't like it as much as some of my outs are likely dead.

At the table it does not matter if you are 85% or 81%. If think you are ahead then you play the hand.

A common approach is to range your opponent (e.g. 88+) and get that equity versus your hand. If they call a raise from middle you would give them a different range than if they open limped from middle. At a live table you cannot run an equity calculation but you can count the number of hands you are ahead and number of hands you are behind. It turns out to be a pretty good equity calculation.

For example pre if I have QQ I know I am about 50 50 against TT+ AKs. If I think they have a weaker range then call. If I think they will only play KK+ in that spot then fold.

Since you must make assumptions about your opponent having exact statistics is not that important. You can run exact statistics later to analyze you play.

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Probability is about knowledge. It is a measure of how certain you can be that a proposition is true, from your point of view, based on all of your knowledge. We assign a value of 0 to mean "I am certain this is untrue" and 1 to "I am certain this is true", and other values in between.

Note that this means there is no such thing as the probability of an event--only the probability of an event from some observer's point of view. You can see this trivially by noting that if you fairly shuffle a deck, but before dealing out a hand of poker you give the deck to someone to look through before you deal. Now, as you deal the hand, the probabilities of events for the players will play out normally. You should still count your pot odds for that draw the same way. But there's clearly no bet you can offer the man who looked at the cards--from his point of view, all events are either 0 or 1. He has complete knowledge.

Let's say I fairly shuffle a deck¸ and then say "For a $1 bet, I'll give you $50 if the top card of the deck is the Ace of Spades". You should decline that bet, because the probability is 1/52. Now I deal off the top 10 cards into a separate pile, and offer the same bet. Now there are only 42 cards in the deck, but the probability from your point of view is still 1/52. If we repeated this scenario a million times, and you made the second bet each time, you'd win about 1,000,000/52 times, despite the fact you were betting on a 42-card stack. There are still 52 cards unknown to you--it makes no difference if they are in the main pack, across the table, or out the window.

Now let's say I take that pile of 10 cards I dealt off and turn them over, and none of them is the Ace of Spades. Now you should take the bet, because you have new information. The position of the Ace in the pack didn't change, but you have received new information about where it isn't, and that affects your probability.

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