Re: mistake?
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I would give you 3 outs on the flop. 2 for the two 7´s + 1 for str8+flsh.
So you need 14:1 to call.
You need to contract 2 big bets to make this breakeven, which is very likely.
Lets take the worst case scenario. The flop is capped and 3 players sees the turn (including you). That would give you 16:4 = 4:1. This means that you would have to contract 5 big bets on the turn and river to make it breakeven.
Even the worst case scenario seems like it won´t cost you to much. So i would call it.
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The "what's wrong with my math" is simple.
Given 3 outs you need about 14:1 is correct.
Hero is currently getting 9:1 to call. Assuming he is peeling here, he needs to win 5 SB when he hits his set. That's not so bad, except for the real fear that it gets raised behind him.
Suppose Hero knows it's going to get raised. Assuming that you get a couple other players to the turn, his odds are now something like 14:2 = 7:1. What must he do in implied odds to get up to 14:1? You can't look at 7:1 and work your way up from there, because that number has been rescaled. He is investing 2, so needs to win 28 total. Going from 14:2 to 28:2 is another 14 SB.
In the capped case, you're looking at something like 20:4, which needs to get up to 42:4 to break even, which is a whopping 22 extra SB AFTER the turn card. Good luck.
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