Common turn problem - QQ

[yourface]

sry, wasn't clear with the 30% thing. plz check it out again

also I forgot to edit in that I wasn't including villain calling with busted broadway draws, though that is possible

edit: and obv we don't have 30% eq when villain raises our river bet. a better way of putting it would be we have 30% equity vs villains calling/raising range when we bet the river

[vmacosta]

ok, your edit clarifies things.

Can you please include the portion of the range that folds to your river bet? Because the relative size of that range is pretty important here imo. Otherwise it's hard to know how to interpret your %bluffs in:

c/f if %bluffs < 12%,
b/f if 12% < %bluffs < 30%
c/c if 30% < %bluffs

[Nick C]

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I think we can all agree that the best turn line is b/f

if we get called on the turn it leads to a more interesting river decision. the PPs that we can get value from are outweighed by the ton of Ax combinations that a LP can have, plus he will sometimes be slowplaying a monster like trip Ts.

messing around with stove I think we have around 30% equity on a brick river. also I don't expect villain to value bet any of the hands we beat after we check to him. I do think that he'll probably VB every hand that beats up unless he can show up with KK

the pot size will be ~7BB, so if villain is bluffing more than 1/8 of the time (7 times we lose 1BB, 1 time we win 7BB = breakeven) we should be calling. 1/8 is 12.5% of the time.

so if we expect villain to bluff less than 12.5% of the time we should c/f. if we expect him to bluff between 12.5% and 30% of the time we should b/f because we lose less on that river bet. if we expect him to buff more than 30% of the time we should c/c.

does that look right?

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In this scenario, we have no good options at all (our hand is simply worst too often, and we have no folding equity) and the whole exercise is about limiting the damage. But sometimes that's all you can do, so here goes . . .

In a pot that's 7 BB big after a river bet from Villain (which is about right, especially after taking the rake into account), his theoretically optimal bluffing frequency is to have the best hand 7 out of 8 times that he bets. This means that if he's betting the best hand the full 7 out of 10 times that he has it, he should theoretically bet 1 out of his 3 losers for balance. And if he does this, all we can do is either bet-fold or check-call, depending on how many of those 30 losing hands Villain will actually call with (if he'll call with more than 1/3 of them and will never bluff-raise, then bet-folding is the best play). The reason check-folding is bad (in this scenario) is that the bet we "save" by folding the worst hand those 7 out of 10 times is wiped out by that 1 time in 10 that we fold the pot away, and meanwhile we never win a river bet with a check-fold and also never snap off a bluff.

As Villain's bluffing frequency decreases, bet-folding becomes more attractive (check-calling is now bad), but at some point this play becomes inferior to check-folding. (If Villain would always call with his losing hands, then check-folding would overtake bet-folding when Villain started betting less than roughly 6.67 of his 30 losers. But having him always call with his losing hands does seem unrealistic, so for practical purposes that 6.67 cutoff point must be at least a little higher.)

As Villain's bluffing frequency increases, the case for check-calling starts improving. Nevertheless, if Villain were calling 100 percent if we bet, check-calling would never be superior to betting.

Er, basically, I guess I'm saying you haven't really provided enough information to work out the scenario. We need to know how many of those worse hands Villain will call a bet with.

[Nick C]

Okay, your edit changes things. I think it's much more realistic now too (I thought having the best hand on a river brick only 30 percent was too pessimistic for Hero's QQ.)

Anyway, though, the information that is now missing is how often (if ever) Villain will bluff a hand he wouldn't have called with. If he'll never do this, and also will never bluff raise, then check-calling will never be superior to betting in the scenario (edit: well, so long as you have Villain betting all of his winning hands, that is -- this stuff can get very complicated [img]/images/graemlins/laugh.gif[/img]).

[Nick C]

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if we expect him to buff more than 30% of the time we should c/c.

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Since this is not possible unless Villain is betting some hands he wouldn't call with, what you're basically implying is that we should check-call if Villain will bet anything he would have called with while also betting a few pure bluffs. And I agree with that, based on your assumptions.

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if we expect villain to bluff less than 12.5% of the time we should c/f.

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If I'm understanding your numbers correctly, your cutoff point is about 6 percentage points too high here.

Edit: And, all right, I guess I should explain why. First of all, the 12.5 number is off; for "optimal" bluffing frequency relative to the pot size, the number should be 1/7 of 70 percent (the 70 percent being the winning hands he's betting), or 10 percent.

Also, though, even if Villain doesn't bet quite as often as is theoretically optimal, he still gains when he bets the worst hand and we fold. So it takes a while for check-folding to overtake bet-folding, given all of the assumptions in the scenario. The reason is, basically, that although we're betting with the worst of it, at least when we bet-fold, we never surrender a pot we should have won to Villain (and this of course assumes he never bluff-raises -- if he does bluff-raise sometimes, then that could change things dramatically). And it takes quite a few saved bets to make up for the occasionally sacrificed pots.

[yourface]

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if we expect him to buff more than 30% of the time we should c/c.

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Since this is not possible unless Villain is betting some hands he wouldn't call with, what you're basically implying is that we should check-call if Villain will bet anything he would have called with while also betting a few pure bluffs. And I agree with that, based on your assumptions.

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he will not call with many busted draws but may bluff them given the chance. by "bluff more than 30% of the time" I mean more than 30% of his river bets being bluffs.

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if we expect villain to bluff less than 12.5% of the time we should c/f.

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If I'm understanding your numbers correctly, your cutoff point is about 6 percentage points too high here.

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pot is 7BB after villain bets the river. the EV calculation for the river is

7BB*x - 1BB*(1-x) > 0
8BB*x - 1BB > 0
8BB*x > 1BB
x > 1/8
x > 0.125

am I missing something?

[Nick C]

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by "bluff more than 30% of the time" I mean more than 30% of his river bets being bluffs.

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Yeah, and if 70 percent of his "showdown" hands are winners and he bets all of them, then he can't bluff more than 30 percent on the river unless he's also betting some non-showdown hands.

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if we expect villain to bluff less than 12.5% of the time we should c/f.

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If I'm understanding your numbers correctly, your cutoff point is about 6 percentage points too high here.

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pot is 7BB after villain bets the river. the EV calculation for the river is

7BB*x - 1BB*(1-x) > 0
8BB*x - 1BB > 0
8BB*x > 1BB
x > 1/8
x > 0.125

am I missing something?

[/ QUOTE ]

I tried to explain in my edit. Anyway, though, the thing is, Villain is not betting the entire 100 percent of the "showdown" hands you've assigned to him. He's only betting 70 out of those 100 hands, plus a few of the losers. So if he bets 12.5 of the losers, we'll win 12.5 out of 82.5 times we call (about 15.15 percent). This is better than the 12.5 percent we need to break even, so we have a call, and Villain is bluffing too often from a theoretical standpoint. (Edit: Nevertheless, bet-folding would still be better than check-calling given our assumptions, because Villain will call with more losing hands than he'll bet himself.)

So that's why his optimal bluffing frequency should be 10 percent of the showdown hands you've assigned to Villain (assuming he's never betting any non-showdown hands, that is). Basically, whatever hands he's betting, theoretically 1/8 of them should be losers. If he were only betting trip T's but was checking aces up, for instance, then he'd need to start betting a much smaller percentage of his losers to remain theoretically optimal with his bluffs.

Meanwhile, just because Villain starts only bluffing 9.8 losers versus 70 winners doesn't mean check-folding instantly becomes better than bet-folding. He does still gain on those bluffs, and bet-folding was actually quite a bit better than check-folding at that 10-bluffs-per-70-value-bets cutoff point (basically because by bet-folding we still get value from all of Villain's losing showdown hands and meanwhile never sacrifice the pot to one of his bluffs).

Okay, and I do want to emphasize one thing: If Villain bluff-raises sometimes, then that changes everything. The reason I'm emphasizing this is that in our scenario we've made bet-folding a completely safe play, in that it never costs us any more than that one last bet we put in (and we've probably done this more or less appropriately, since Villain is very loose/passive). However, versus a river LAG (instead of our loose-passive in this hand), bet-folding a good hand in a big pot is incredibly risky.

[TheHip41]

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