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Old 03-01-2014, 02:41 AM   #8
Spongeboobies
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Join Date: Dec 2013
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Re: 3k post: Overbetting.

Expert Heads Up NLHE has a really good discussion on optimal river play given a certain percentage of slow plays in villain distribution. For now we are still going to shove. Villains total defending frequency including traps is going to be P/(S+P); P=Pot, S=Stack. So when deciding to shove at a certain stack size with our value hand we need to decide which term is greater for our villain, their their trap frequency T or their bluff catching frequency P/(S+P) - T. If T is greater, we are losing money on our shove with our Value hands so we need to start considering smaller bet sizes. This smaller bet size increases Villains optimal bluff catching frequency and in a lot of cases this can still be an over bet. Now Villain has the option of raising over top of our smaller bet size with their Traps + some bluff catchers to make our Value range indifferent to calling or folding. Villains bluffing frequency in this case is X = (S-B)/(2S+P); where B is our new bet size, and X is their bluffing frequency. As stated in your earlier discussion, our EV for this decision is now going to be 0 once Villain shoves over us and our overall EV will be our stack - Bet, S-B. Now Villains jamming Frequency is T+X and their bluff catching frequency is P/(S+P) - (T+X). With our Value hands we lose B every time villain shoves and win the pot every time they bluff catch, so intuitively we need to choose a bet size that is going to be most EV for us. We can now set up an EV equation for betting, in the book it is written EVbet = (S-B)(frequency Villain shoves) + (S+B+P)(Frequency Villain Bluff catches) + (S+P)(Villain folds). The author uses calculus to find the maximum bet size given effective stacks in Pot sized bets and % Traps in Villains range

Anyways the results are that if Villains Stack = 2 Pot sized bets it is still optimal to shove on the river if 10% of their range is traps. If stacks are 10 Pot sized bets now our optimal bet size is going to be less than 1 pot sized bet.
Lets say Villain holds 5% traps and effective stacks are around 3.5 Pot sized bets, it is still correct to shove. Its a pretty neat graph in the book.

Last edited by Spongeboobies; 03-01-2014 at 02:52 AM. Reason: I forgot's to add something
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