Simple Math -- Your Set vs. Apparent Flush

Situation:

Hero has $200. Hero has 8-8. Six players call a mini-raise to $4. Flop:

2c 8c 3c

Hero bets $20. Table folds around to CO who has about $300. CO pushes. Hero's play?

Analysis

If you think there is around a 70% chance that he's already got the flush, this is still a CALL.

First, calculate your pot odds. Assuming that you sat down with the $200 max, the pot is:
$24 PF betting
+$20 your flop bet
+$20 his call
+$176 his raise (what you've got left)
=$240 pot

It costs you $176 to call, so you're getting 1.36 to 1 on your call to win a $240 pot.

Let's calculate for two scenarios, which are very likely the case in this hand:

1. He's already got the flush, with something like Ac 7c.

Your probability of winning this hand is 34% (verified by PokerStove). So, your EV of this hand:

34% x $240 = $81
66% x -$176 = -$116
81 + -116 = -35
Total EV if you call and he already has the made flush is -$35.

2. He's got the Ace-high flush draw, with somethinh like Ac7d.

Your probability of winning this hand is 71% (verified by PokerStove). So, your EV of this hand:

71% x $240 = $170
29% x -$176 = -$49
-116 + 81 = $121
Total EV if you call and he's on the flush draw is $121.

Now, the critical question -- what do you think the probability is that he already has the made flush?

First, let's say that you think there's a 60% chance he has the made flush, and 40% chance he's on the flush draw. The total EV of this situation is:

60% x -$35 = -$21
40% x $121 = $48
Total EV = $25 ----> CALL!

Now lets say that you think there's a 70% chance he has the made flush:

70% x -$35 = -$24
30% x $121 = $36
Total EV = $12 ----> CALL!

What's the break-even point? At about 77% chance he has the made flush, then its a coin-flip in terms of EV:

78% x -$35 = -$27
22% x $121 = $26
Total EV = -$1 ----> Fold.

What this means in practical terms --
Let's say that you are in this exact situation 100 more times, and there's exactly a 70% chance he already has the made flush. If you call each of those 100 times, you will win about $1200 total.