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A Runner-Runner flush question

  
 
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Ragnar4
Old 06-09-2007, 10:09 PM     Post subject: A Runner-Runner flush question #1 (permalink)  
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Lets say that:

Hero has Ah 2h on the button.
Villian has Jd Ts a straight you know this because he rolled over his hand on the flop. You know for a fact that he's going to bet/raise every chance he gets.

Board is 9h 8d 7c

How many bets need to be in the pot for you to peel to see the turn profitably?

The first argument I want to make is 23-1. Only a flush can win here, and we all know you only catch runner runner to the river 23-1 against.

The second argument that may stand some debate is 5-1. The reason being is that on the turn, you'll get one of your hearts 17.1% (5-1 equity is 16.5% of the time). If you catch your heart, you've got more than the equity to see the river. But if you miss, you fold and it only cost you one bet.

Discuss.

edited because I'm really tired, and didn't have a RR flush possibility on board.
The older I get, the more I start wondering; Just what in the hell is going on here?
 
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krimson
Old 06-09-2007, 11:01 PM     Post subject: Re: A Runner-Runner flush question #2 (permalink)  
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krimson
Assuming that you mean that you actaully have a RRFD (say A2s of anything but hearts on that board) then think of it this way: you have 10 outs to "hit" the turn, but when you do you only win about one fifth of the pot. So there need to be roughly 25 small bets in the pot. (With more care the exact answer comes out at 226/9 small bets.)
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sinky
Old 06-11-2007, 09:57 AM #3 (permalink)  
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sinky
As you said the odds of hitting a runner / runner flush are (10/47 * 9/46) = 4.16% or 23 to 1.

You say that opponent will bet or raise at every opportunity, so you have good implied odds. 1BB from the turn call and hopefully 3BB from the river. So 8 SB extra in total.

78.7% of the time you will miss the turn and fold costing you 1 SB
17.1% of the time you will hit the turn but miss the river costing you 3SB.
So on average it will cost you 1.3SB.

With a 23/1 chance of winning you need the pot to be greater than (1.3*23) = 29.9 SB. We have estimated 8 extra SB when you win, so in order to call the flop you need 22 SB in the pot.
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