In this hand there were a couple of very loose aggressive players with large stacks on my table, so I had decided to move to another table with higher stakes, but before I left, I was going to play one more hand just to see if I could take a shot at a really big pot. If you cannot see it, my hand is Jack of Spades and Ten of Hearts.

Mr. Aggressive made a large bet preflop, which I thought could be a bluff, and then a huge bet on the turn, which was called by a second player so maybe he had a flush, or another hand, or a bluff could not be ruled out, or maybe not, so possible another Ten could win me the pot, and if a spade came down, there is a good chance that I have the better flush, but there was just one other card that would do the trick and get the rest of my chips inâ€¦ Given the pot odds and with 10 possible outs (some of which might not be outs) I should have normally have folded, but like I say, this was my very last hand on the tableâ€¦

Situation dictates everything really, for me, J 10 is a good hand but easily beatable, so Iâ€™d probably fold to big raises before the flop in a ring game, but fair play to you for sticking in there and you got yourself a nice reward from it. Canâ€™t beat those good moments.

Based on the cards that we know the odds of the final card being the Queen of Spades would be 45 to 1, but this can only be an approximation, because we donâ€™t know if the opponent had the Queen of Spades, or whether the Queen of Spades was already folded by another player. In other words we donâ€™t even know if it was in the deck.

The odds of hitting any spade or a Ten would be 11/46, but again we donâ€™t know how many of those out cards are actually still in the deck.

Incidentally a point I have never seen discussed in a poker bookâ€“perhaps I just never noticedâ€“is that when it comes to longshot draws, your chances could be somewhat improved on a smaller table versus a full 9-person table, because there will be less cards taken out of play and already mucked.

I donâ€™t think the # of players is relevant here (unless you somehow know what they have), because we arenâ€™t talking about THE (absolute) odds, but â€śYOURâ€ť odds, based on what YOU (subjectively) know in a limited-info situation.

Imagine youâ€™re playing 22-handed. Itâ€™s a â€śliveâ€ť type table so cards are getting burned. 44 cards get dealt preflop, 5 cards are dealt thereafter plus 3 burn cards. That is, every single card is ultimately â€śin playâ€ť.

Are â€śyour oddsâ€ť of pairing the board any different? Now imagine you can peek at 11 playersâ€™ hands. Then what are â€śyour oddsâ€ť?

Having more/less players at the table is significant b/c other players w/live hands (eg behind you) can each have any selection out of the cards you know are â€śout thereâ€ť, that is, in the deck OR in their hands. This is the underpinning principle of positional play, isolation, etc.

But the number of players never changes â€śyour oddsâ€ť of getting any given draw, unless you â€śknowâ€ť what they have (either literally by cheating or virtually b/c you read them that well). Just like you know that if a Q-hearts is on the board it isnâ€™t in anyoneâ€™s hand nor can it be drawn later.

The classic game theory Monty Haul â€śparadoxâ€ť is illustrative of the notion that â€śyour oddsâ€ť arenâ€™t absolute but based on the information you have (which itself may evolve).

When you pick door #1, there is a 2/3 chance the car is behind doors #2 or #3. When Monty reveals a goat behind door #3, there is still a 2/3 chance the car is behind doors #2 or #3, but YOU HAVE NEW INFORMATION, namely, there is no car behind door #3, thus there is now the same 2/3 chance of a car but now itâ€™s behind door #2 ONLY.

As noted in the article, literal PhDs break their brain on this.