It is my experience that playing everything up to 20$ tourneys many casino game players have little idea of pot odds. They have memorised that 22 is maybe 52% over most overcards, they know the odds of a straight draw and a flush draw and a straight flush draw, but that is about it.
They either dont know how to calculate pot odds from first principles or just can’t in the time frame available.
I won’t say that I can calculate to the percentile during live play online but my estimates are almost always accurate to the nearest 5 percent. I will start by showing beginners how to calculate pot odds and then show others some more advanced concepts I am trying to formulate with them for tourney play.
A common scenario is say you have A8 of heart, the flop is 4H KH 7C. You have 2000 chips, 400 in the pot already, first to act you bet 500 and are reraised all in by someone who just has you covered. Do you have pot odds to call?
The chance of catching a flush is the number of hearts unaccounted for (9) divided by the number of cards unaccounted for (47) +(45-9)/45 (chance of not getting a flush on turn) * 9/46 = 35% almost exactly.
In other words it is the chance of catching a flush on the turn plus the remaining chance of catching a flush on the river otherwise you are counting heart on turn + heart on river twice. It is important to not that this is just your chance of catching a flush not of winning.
Let’s pretend though that it is the same thing for the next calculation. You then must multiply the stack you would have if you catch the flush with the odds of catching. If this is greater than your stack if you fold – then you should fold. So .35*(pot of 1400 plus 1500 chips you have plus their 1500 equals 4400) = 1540 making a call the better decision under normal circumstances.
Normally you can place the opponent for holding certain cards then you would be dividing by 45 (turn) and 44 (river). It is key to calculating pot odds in this sort of scenario to realise that you can win without getting a flush. That is the part that most people dont twig and when you catch a flush they will say you lucky donkey when you might have had 8 or more additional outs.
Lets say he has AKo (no hearts) – you win with any flush unless he catches a full house and you win when you catch trip 8s and he does not catch another K – you also win if you catch a straight. So you will win
1) 1/45 (7 hearts) *42/44 (winning on everything except the two remaining kings) +
2) 8/45 (remaining cards giving flush +
3) 3/45 (remaining eights) * 33/44 (every heart + the two remaining 8’s) +
5) 2/45 (remaining 7’s) * 8/44 (7 of hearts will give him a FULL H) +
6) 8/45 (5or 6) * 13/44 (flush cards plus the 4 cards that will give a straight +
7) 2/45 (a king) *8/44 (hearts other than 7) +
8) 21/45 (remaining cards *9 (flush cards) /44.
It is possible that one number here or their might be wrong but that is the basic position and in this case it will not make much odds but because it is such a marginal decision it could affect whether it is a sound call. There chance of a full house seems greater than the chance of either getting the straight or of three 8’s being the winning hand so possibly no longer pot odds to call (particularly after house cut) but it is so borderline (34.09 is the probability needed to call (no of chips if you fold / no of chips if you call ) – so it is very close.
In some positions though it is a clear call ie if 700 chips already in pot – or if say he could be put at say a low pocket pair where you would win with either of your cards paired up most times in addition to the flush draw and long odds straight draw less a possible long odds straight draw for him.
Ok that was the simple stuff – remember that chips if fold over chips if call (*100) is the percentage you need to call.