Can anyone give me an idea about the odds that should be considered in the following situation:

- 9 handed live tourney table
- You are 2nd in chips at the table on $50 SB
- 3 limps to you pre-flop including the button
- You call with 5s-9s
- BB checks for 5 players in pot of $500
- Flop is 3s-As-Ks

Questions are:
1) What are odds one of the other 4 players has flopped bigger flush than you?
2) What are odds that one of other 4 players has 10, J or Q of spades and will catch a 4th spade on the board?

Not sure if I played this scenario well recently and hoping explanation of the math will improve my action if it comes up again. Thanks for your thoughts and/or strategy advice about actions to take in this situation...

1) Depends on their limping ranges. Typically limpers could have all kinds of spade hands here. It would be different against an utg raiser who couldn't hit a flush on an AKx board. It happens, but it is rare to be against a higher flush in this spot.

2) Depends on how many players are in the pot, their limping ranges, and how many of them hold a spade. If more than one has a spade(likely) then the cance of them drawing out is less than if it were heads up.

I'm interested if anyone wants to actually give the limpers ranges and figure out the math, but I'm lazy. Sorry for the non mathematical response.

Nothing to be sorry about Bob - thanks for the thoughts. I didn't know any of the ranges (was only 2nd level of blinds). Turns out the only stack on the table, the button, limped with Q-8 spades and I was drawing dead when I bet to try to get 4-flush hopefuls to fold, and moved all in on his raise that I read as an Ace or K trying to get me to fold a draw. Maybe there were 15 spades in the deck lol, but I was not happy to flop a flush and be 100% dead at the same time. Part of why I ask about the odds is that if it's as high as one in ten, read or no read, I shouldn't have shoved. If it's less than one in 25 (or similar), I'll chalk it up to bad variance (or karma ;-)...

I have a simulation program that can answer these questions.

1. What are odds one of the other 4 players has flopped bigger flush than you?
That means at least one player with 2 spades with at least one being ten, jack or queen. The simulation result was 6.58%.

2. What are odds that one of other 4 players has 10, J or Q of spades and will catch a 4th spade on the board?
That means that at least one of the four has one spade ten or higher. This has probability 38.5%. The probability another spade will fall on the turn is at most 3/47. (If two players have one spade, then there are only 2 remaining spades, etc.) Both events together then have probability no greater than 2.5%.

Note these results are strictly combinatorics. Reads, prior bets, bet sizes, etc. could be used to adjust the pure math results.

You're weren't exactly 100% dead. A 2s + 4s turn and river would backdoor a str8 flush, so you were actually only "practically" 100% dead, so there was still hope!

I tried to do the math in my head and just got confused , but I came up with something like 8% , close enough.

A decent approximate method can be used.

There are 8 remaining spades, 3 of which are ten, jack, queen. The number of ways one player can have 2 spades, and at least one of which is T, J, or Q is

C(3,1)C(5,1)+C(3,2)C(5,0)=18

The total number of hands for a player from the deck of 47 is C(47,2) = 1081. Therefore the probability one player has a higher flush is 18/1081 = 0.01665. An upper bound for at least one of four players having a higher flush is 4*0.01665 = 0.0666, or 6.66%.

For a lower bound, no higher flush for one player has probability 1-0.01665 = 0.98335. Raising that to the fourth power is an upper bound for all four players not having a higher flush. Subtracting from 1 gives a lower bound to the higher flush chances, and the value is 6.496%.

Note the simulation result of 6.58% is in between the two bounds.

Thanks for the math/insight folks. I fell better about losing now lol (wrong read against an aggressive opponent, but I wouldn't be wrong more than 1 in 15 or so times which I can live with)...