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11-28-2017 , 04:42 PM
Quote:
Originally Posted by Maroel
Actually, it's the opposite.

A will always lose EV if he decide to bluff less against any calling frequency < 50 %, losing more against the smaller calling frequency (0%), and less against the biggest optimal calling frequency (50%) where he is indiferent.

Only in the optimal calling frequency of B (50%), Player A is indiferent to bluffing all his bluffs or none.

This is because any bluff will win money by betting pot size against any calling frequency < 50%, summed with the fact that by checking those bluffs player B win the entire pot with his bluff catchers, so altought Player B lose a bit of money by calling a non balanced bet with his bluffs catchers, don't betting his bluffs actually makes player A lose EV against any calling strategy of B < 50%.

So because the best strategy for player A is always betting all his bluffs, against any Player B calling strategy < 50%, that's what he will always do.

And against that strategy, Player B can call with any frequency between 0% to 50% and player A can't do nothing to improve (again, if he decides to bluff less, he loses ev against any of those strategies)

Only if player B decides to call more than 50%, Player A can deviate to don't bet any bluff and actually improve EV. Thus, calling > 50% can't be an optimal strategy for player B, and calling any from 0% to 50% are optimal strategies for player B.

P.D: A calling frequency < 50% could only be exploited by a player with a bluff range distribution > 1/3, then he would shift to bluffs all his bluffs and improve ev compared to betting balanced, but in this toy game it is not an option for Player A because of his range distribution.
I need to do the math and stop just trying to think about it without math.

To me the idea that A can bet pot and make less money makes no sense. Yes his bluffs don't steal the pot as often but B has to be paying of A's value bets too frequently because B is not getting the proper equity to call vs A's distribution of betting hands.

Any way I'll do some math later and probably arrived at the same conclusion. Haha.
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11-28-2017 , 05:31 PM
Quote:
Originally Posted by just_grindin
I need to do the math and stop just trying to think about it without math.

To me the idea that A can bet pot and make less money makes no sense. Yes his bluffs don't steal the pot as often but B has to be paying of A's value bets too frequently because B is not getting the proper equity to call vs A's distribution of betting hands.

Any way I'll do some math later and probably arrived at the same conclusion. Haha.
How would A ev improve by not betting ev+ bluffs? (Against any calling strategy from player B < 50%, Player A makes automatic profit with his bluffs).

You don't need math to get that haha

But do it anyway.
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11-28-2017 , 06:05 PM
Quote:
Originally Posted by Maroel
How would A ev improve by not betting ev+ bluffs? (Against any calling strategy from player B < 50%, Player A makes automatic profit with his bluffs).

You don't need math to get that haha

But do it anyway.
Idk I'm dumb sometimes? I was just thinking Idk how B would make money by incorrectly calling with bluff catchers even if he knows A is underbluffing. So if B is losing money on the call it has to go somewhere which should be to A.

Maybe my mistake is in thinking it's always enough to compensate for A stealing the pot with some frequency with his bluffs.
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11-28-2017 , 06:31 PM
Quote:
Originally Posted by just_grindin
Idk I'm dumb sometimes? I was just thinking Idk how B would make money by incorrectly calling with bluff catchers even if he knows A is underbluffing. So if B is losing money on the call it has to go somewhere which should be to A.

Maybe my mistake is in thinking it's always enough to compensate for A stealing the pot with some frequency with his bluffs.
Player B would make the most money by never calling if player A is underbluffing.

So yes, the money he loses by calling goes to player A.

But player A doesn't make the most money by underbluffing against any calling strategy from player B <= 50%.

If player B never calls, player A should bet all his bluffs (not betting insure he losing the pot)

If player B calls 25%, he should bet all his bluffs (they are automatic profitable)

If player B calls 50%, he can do whatever he wants with his bluffs because they are indiferent, ev doesn't change. But any strategy that is not betting all the bluffs are exploitable (by player B never calling with bluff catchers)

Thus player A will bet all his bluff always.

Player B can call with any frequency between 0 to 50% with the same ev (because player A will always bluff against any of those strategies) and player B will be indiferent with his bluff catchers to a balanced bet always.

Last edited by Maroel; 11-28-2017 at 06:37 PM.
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11-28-2017 , 08:03 PM
Yeah I realized were I got confused as I have done this math before but was only focused on A's bluffs and indifference. This time I was trying to incorporate the value betting and was doing so incorrectly.

Not sure why my brain just doesn't work sometimes but hopefully I'll forget that it doesn't and not care anymore haha.
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