Flush Draw Implied Odds Problem

[Zangief]

http://www.flopturnriver.com/phpBB2/...ic.php?t=18345
The above post got me thinking about the implied odds of flush draws. So I pose a problem:

The pot is 10xBB.
My opponent and I each have 95xBB.
I know I have the best hand now.
I know my opponent has a draw that will hit on the turn 1-in-5 times.
I will always lose a showdown if my opponent's draw hits.
My opponent will fold the turn if he misses, but go all-in if he hits.
I will always call an all-in.
I am last to act and my opponent has checked to me after the flop.

How much must I bet to make sure I don't lose money from this situation?

(Or what bet size makes this EV = 0?)

I'll post a solution later if no one else gets it first.

[lowBoy]

2.5xBB would get him the exact right odds for hitting his draw on the turn.

So with a 2.5BB bet, you'll either lose 92.5BB %20 of the time or win 15BB 80% of the time.

-92.5BB * 0.2 = -18.5 EV
15BB * 0.8 = +12 EV

You'd have to bet 6BB to keep things very close to even. Add in fold equity from the 6/10ths pot bet, and you're looking +EV IMO.

-89BB * 0.2 = -17.8EV
22BB * 0.8 = +17.6EV

I suppose you'd have to bet around 6.something_small to keep it EV=0... but this is pretty damned close and would be +EV with the fold equity.

This is based on from what I remember of EV calculations... so it could be horribly wrong.

[krimson]

Your equity if op folds on flop = +10
Your equity if op calls bet B on flop = 4/5*(10+B) - 95/5 = -11 +4B/5

Thus betting anything less than 5/4 * (10+11) = 26.25 is suboptimal. If you bet more than that it is correct for op to fold. If you bet less he has implied odds to call.

Betting anything less than 5/4 * 11 = 13.75 is actually worse than just folding on the flop.

[Zangief]

Looks like this is the right answer:

Your equity if op folds on flop = +10
Your equity if op calls bet B on flop = 4/5*(10+B) - 95/5 = -11 +4B/5

Thus betting anything less than 5/4 * (10+11) = 26.25 is suboptimal. If you bet more than that it is correct for op to fold. If you bet less he has implied odds to call.

[Molinero]

My opponent will fold the turn if he misses, but go all-in if he hits.
I will always call an all-in.

Maybe I'm missing something, but if your op goes all in when he hits, why would you call? Seems like a pretty obvious fold here, if he pushes 95BB at a 10BB pot after the third flush card hits, and you had him on a draw.

What did I miss?

[DoGGz]

My opponent will fold the turn if he misses, but go all-in if he hits.
I will always call an all-in.

Maybe I'm missing something, but if your op goes all in when he hits, why would you call? Seems like a pretty obvious fold here, if he pushes 95BB at a 10BB pot after the third flush card hits, and you had him on a draw.

What did I miss?

He can't fold hands because that would be to easy.

[Zangief]

My opponent will fold the turn if he misses, but go all-in if he hits.
I will always call an all-in.

Maybe I'm missing something, but if your op goes all in when he hits, why would you call? Seems like a pretty obvious fold here, if he pushes 95BB at a 10BB pot after the third flush card hits, and you had him on a draw.

What did I miss?

This is not supposed to represent a real-world situation; it is supposed to be a theoretical problem designed to answer these questions:

1. If I am committed to my hand for my entire stack, how much must I raise to make sure drawing to a flush is an error for my opponent?

2. Stated from the opposite side: If I believe an opponent is committed to his entire stack, how much can I call with a flush draw that will still be profitable?

I am not suggesting that anyone should play like this. But I think this information could be useful in situations similar to those stated in the original problem.

[Molinero]

My opponent will fold the turn if he misses, but go all-in if he hits.
I will always call an all-in.

Maybe I'm missing something, but if your op goes all in when he hits, why would you call? Seems like a pretty obvious fold here, if he pushes 95BB at a 10BB pot after the third flush card hits, and you had him on a draw.

What did I miss?

This is not supposed to represent a real-world situation; it is supposed to be a theoretical problem designed to answer these questions:

1. If I am committed to my hand for my entire stack, how much must I raise to make sure drawing to a flush is an error for my opponent?

2. Stated from the opposite side: If I believe an opponent is committed to his entire stack, how much can I call with a flush draw that will still be profitable?

I am not suggesting that anyone should play like this. But I think this information could be useful in situations similar to those stated in the original problem.

Fair enough: Raise everything. That oughta do it.