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  #1  
Old 12-22-2005, 05:05 PM
A_PLUS A_PLUS is offline
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Default More Math Shortcuts (Inducing a bluff)

This idea comes from trying to answer a question in Exitonly's post Exitonly is a call station



Question

We have taken a line such that we believe that we are ahead on the turn. The problem is, we are out of position and the pot is getting large. We have checked, our opponent bets, should we take the pot with a push (we know we can), or should we let him see a free river with the chance he will bluff off the rest of his chips. Lets make things easier and assume that their are no big draws on board.

**This general set up can be used to think about a lot of hands. Once we decide we arent going to fold. The range of hands where the villan will make the same decision, regardless of what you do, can be safely ignored. We only care about his potential hands where our line matters. This is why I assume a push would work, b/c without huge draws on board, hands that call our push would likely have gotten all-in regardless.


**We will also assume that the only reasonable bet for the villan on the river is a push. Given the shallow stacks of most online MTTs, I think that is very reasonable.

What do we want to know?

How often will the villan have to bluff the river to make giving him a free card a good idea?

What do we need to know?

How many outs the Villan has against you

Yep...thats it.

[0-5 outs]
% of time he must bluff = (outs x 2%) * {1+ (Pot when you call / His remaining chips)}

[5+ outs]
% of time he must bluff = (outs x 2.5%) * {1+ (Pot when you call / His remaining chips)}

Look at his remaining stack, and fill in the blank
The pot is ______ times as large as his stack
-add 1
-multiply that number by (outs x 2~2.5)

I know most of us rely on our 'gut' to decide this play, but it is always nice to know the kind of assumptions our gut is making. Just looking at the equation should confirm your poker intuition. As the pot gets large compared to our stacks, the rate at which he must bluff the river goes up. The more outs he has, same effect.
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  #2  
Old 12-22-2005, 05:43 PM
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Default Re: More Math Shortcuts (Inducing a bluff)

Does your premise assume that the free card is only enough to make his hand, but not enough to beat us (i.e., he is drawing dead), or are you assuming there is an 8-1 shot that the opponent's card beats us?
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  #3  
Old 12-22-2005, 07:58 PM
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Default Re: More Math Shortcuts (Inducing a bluff)

[ QUOTE ]
This idea comes from trying to answer a question in Exitonly's post

[/ QUOTE ]

I love it how an interesting post always seems to come up during the same day's play. I just had this hand a short while ago. It seems to mirror the concept you are getting at.

Hand #1045xxxx-16 at XXXXpmA-010 (No Limit tournament Hold'em)
Started at 22/Dec/05 18:16:42

PlayerA is at seat 0 with 1805.
PlayerB is at seat 1 with 1660.
PlayerH is at seat 2 with 1410.
PlayerC is at seat 3 with 3025.
Villain is at seat 4 with 1540.
PlayerD is at seat 5 with 1770.
PlayerE is at seat 6 with 1055.
Hero is at seat 7 with 1355.
PlayerF is at seat 8 with 1470.
PlayerG is at seat 9 with 1410.
The button is at seat 8.

PlayerG posts the small blind of 10.
PlayerA posts the big blind of 20.

PlayerA: -- --
PlayerB: -- --
vernally: -- --
PlayerC: -- --
Villain: -- --
PlayerD: -- --
PlayerE: -- --
Hero: Qh Ah
PlayerF: -- --
PlayerG: -- --

Pre-flop:
PlayerB folds. PlayerH folds. PlayerC folds.
Villain raises to 70. PlayerD folds.
PlayerE folds. Hero calls. PlayerF folds.
PlayerG folds. PlayerA folds.

Flop (board: Jc Ad 5h):
Villain bets 170. Hero calls.

Turn (board: Jc Ad 5h 3d):
Villain checks. Hero checks.

River (board: Jc Ad 5h 3d Ac):
Villain bets 225. Hero calls.

Showdown:
Villain shows 9c 9s.
Villain has 9c 9s Jc Ad Ac: two pair, aces and nines.
Hero shows Qh Ah.
Hero has Qh Ah Jc Ad Ac: three aces.

Hand #1045XXXX-16 Summary:
No rake is taken for this hand.
Hero wins 960 with three aces.
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  #4  
Old 12-22-2005, 08:01 PM
schwza schwza is offline
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Posts: 113
Default Re: More Math Shortcuts (Inducing a bluff)

i like it. here's an example:

villain has 2k left, pot is 3k, villain has 4 outs.

pot is 1.5 as big as stack. add 1 to 2.5. 4 outs = 8%, so the answer is 20%. seems reasonable.

my only question is why you multiply by 2 for 0-4 outs and 2.5 for 5+ outs. seems like you should be multiplying by 100/46=2.17 (46 cards left in deck) regardless, and the fudge factor of calling that 2 is always better (and simpler) than 2.5. am i missing something?
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  #5  
Old 12-23-2005, 11:04 AM
A_PLUS A_PLUS is offline
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Posts: 44
Default Re: More Math Shortcuts (Inducing a bluff)

When I solved the equation for the % of time he needs to fold. I got the term [equity / 1-equity], at low number of outs, this is close enough to just straight equity, but it diverges as their outs increase, 2.5 seems to fit well enough until we get over 10-11 or so, which really doesnt come up too often
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