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https://www.pokerology.com/lessons/drawing-odds/

I've seen a lot of poker odds charts like this that specify a hard-coded value for odds based on outs. Is the chart agnostic of the number of players? Wouldn't my odds be greater if there were only 2 players (a large remaining deck) vs 20 players (a small remaining deck)?

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    No, since the number of unknowns is still the same. Commented Apr 30, 2023 at 10:36
  • Can you explain your answer mathematically? If there are 20 players on the table, then there are only 9 cards left post-flop. According to the chart, I could have up to 20 outs. However, there are only 9 cards left.
    – Teddy K
    Commented Apr 30, 2023 at 10:46
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    As long as the other players' cards are unseen, it makes no difference how many cards are left in the deck. Only two of them are going to be dealt (i.e. the turn and river). The turn card has an equal chance of being any of the 47 unseen cards. If you have 20 outs, your odd of hitting on the turn are 20/47. If you miss on the turn, your odds on the river are 20/46. It doesn't matter whether the other 45 cards remain in the deck, are in other players' hands or have been eaten by the dog.
    – Neil T
    Commented Apr 30, 2023 at 10:59
  • With more players you will have less chance of having the best hand but technically the odds wouldn't change since you don't know what cards are in everyone hand.
    – Styxsksu
    Commented May 3, 2023 at 19:12

2 Answers 2

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The number of players doesn't matter when calculating odds.

The thing is, at the flop you have seen 5 cards, and there are 47 you haven't seen. It makes no difference at all if those unseen cards are held by other players, or in the deck.

Example:

Your hand is 6 and 8 offsuit. The flop comes down 7, 9, 2 rainbow.

You have a straight draw with 6,7,8,9 Either a 5 or a 10 will give you a straight.

8 outs x 4 = 32% chance of hitting a straight.

If you have 2 opponents your chance of hitting the straight is 32%.

If you have 15 opponents, your chance of hitting the straight is 32%.

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The poker odds charts are calculated strictly based on a random selection of the next cards. They don't take into account any information about the play to that point.

A player can therefore potentially do better, but there is by no means any "mathematical" way to express this. For example, if the flop is two spades and a non-suited connector, you could guess that people who stay in have cards that could make a hand out of them. And that might let you improve the calculation over the odds charts.

So if there were six players (you and five others) who all stayed in, the chances are great that somebody has a couple spades back. Or cards that will make the straight. So you might infer some information about the cards in other player's hands, and adjust your ideas about the odds for the next two cards. Especially if there is heavy betting.

However, you can't count on this. Anybody could be entirely bluffing. So you can't count on such calculations.

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