Bluffing Frequency Quiz

You're heads-up in position on the river with a bluff catcher. Your opponent goes all-in with a polarized range of nut hands and bluffs.

Suppose you have 30% equity against his range.

How much equity would you have if he bluffed twice as often as he does now?

Back of an envelope calculation, 45%

So if we are saying he has a 50/50 polarized range and we have 30% against that range then if he has a 25/75 range (aka twice as much bluffing) .5*x=.3 x = .6*.75 = .45 = 45%

I haz no idea lul

7/10 hands beat us, we beat 3/10. If he bluffs twice as often that's twice as many hands that we beat. now we beat 6/13. 6/13= 46%

Your equity doubles

Originally Posted by Sasquach991

Your equity doubles

his value range doesn't change though?

If he was bluffing half the time and now he bluffs twice as much, isn't he now bluffing all the time?

Opponents # of combos
20
# of bluffs: proportion of bluffs 8:12

Board: 8d 8c 8h Th Td
Dead:

equity win tie pots won pots tied
Hand 0: 30.769% 30.77% 00.00% 48 0.00 { JJ }
Hand 1: 69.231% 69.23% 00.00% 108 0.00 { QQ+, 64s-63s }

If you add combos to his range that are all bluffs.
# of combos: 28
proportion of bluffs: 16:12


Board: 8c 8d 8h Th Ts
Dead:

equity win tie pots won pots tied
Hand 0: 47.059% 47.06% 00.00% 96 0.00 { JJ }
Hand 1: 52.941% 52.94% 00.00% 108 0.00 { QQ+, 95s, 73s-72s, 64s }


If you just double the number of bluffing combos in the static 20 combo range.
#: of combos: 20
proportion of bluffs: 16:4


Board: 8c 8d 8h Th Ts
Dead:

equity win tie pots won pots tied
Hand 0: 72.727% 72.73% 00.00% 96 0.00 { JJ }
Hand 1: 27.273% 27.27% 00.00% 36 0.00 { AA, 97s, 63s-62s, 54s }


So lolz @ 45%, it's close but wrong.

question is a bit ambiguous, no offense obv

assumptions:
- villain's range is polarized between bluffs and nut hands
- we beat all bluffs but lose to all nut hands
- villain's polarized range is not "balanced" as our equity is only 30%
- therefore 30/100 hands are bluffs and 70/100 hands are nuts

If villain "bluffs twice as often", and he currently bluffs 30/100, then he will now bluff 60/100; and since we beat all bluff hands, our equity is now 60%.

Edit: to clarify - I've interpreted the language used by spoon -- "bluffs twice as often" -- in relative, and not absolute, terms. So the villain is not adding an equal number of bluff combos to the mix; in this case 30+30 / 130 = 46% -- he is actually bluffing double the proportion of combos he was before; 60/100 instead of 30/100.

Yeah, there's a shit load of assumptions we've gotta make, but

In the first instance, villain is betting 7 nut hands for every 3 bluff hands so our equity is 30% since we win 3 / 10 hands.
If he doubles his bluffing freq, its 7 nut hands for 6 bluff hands - 6 / 13 - so our equity is 46%

Originally Posted by Duck Hunter

Yeah, there's a shit load of assumptions we've gotta make, but

In the first instance, villain is betting 7 nut hands for every 3 bluff hands so our equity is 30% since we win 3 / 10 hands.
If he doubles his bluffing freq, its 7 nut hands for 6 bluff hands - 6 / 13 - so our equity is 46%

seems to me that if you're doubling your frequency, and your frequency is 30%, you will now make it 60% amirite? 30% to 46% is not doubling your frequency; the way you calculated it is by adding an equal number of combos to the bluff range while maintaining the number of nut hands (not the same thing obv).

Of course I may just be completely misunderstanding the question and, plz can haz forgivness if I r rong?

Lets say there were ten hand combos in villains range, 3 of which where bluffs. Now he bluffs twice as much. Clearly he will still bet his made hands as well. For this reason, we must change the fraction to 6/13 as suggested by previous posters.


Another way to look at this is say our villain has 20 possible hands with which he can get to the river. In the original scenario he bets 7 of these hands for value, and bluffs with 3 of the other 13 hands. This gives our villain a bluffing % of 3/13 x 100 =23%. In words this means 23 percent of the time he gets to the river with a non nut hand, he fires. if we suggest his bluffing percent doubles he will now be bluffing 46% of his air hands. 46% = 6/13.

Please do not confuse the percent chance villain with bluff with air with our equity. They are not the same.

When we get to river in the first instance, villain is bluffing 30% of the time, or 30 out of 100.

In the second instance, the number of nut hands he has hasn't gone down, surely?

You're saying he now only has 40 nut hands and 60 bluff hands, I'm saying he still has 70 nut hands (why would he have less nut hands because he bluffs more??) and 60 bluff hands

And we are both sat here waiting for someone better than us at poker to correct us!


Edit: dammit bucket beat me to it!!

We should bluff rivers more.

Not if we play 2nl and villains never fold.

True, obv.

Originally Posted by Penneywize

If villain "bluffs twice as often", and he currently bluffs 30/100, then he will now bluff 60/100; and since we beat all bluff hands, our equity is now 60%.

So 30/100 of Villain's value range just magically disappeared?

Originally Posted by Penneywize

question is a bit ambiguous, no offense obv

It's not really, but the average person's understanding of what "twice as often" means gets screwed up when you start talking about percentages, which is part of the point of the thread.

If Bob fucked 6 girls, and Tim fucked 1 girl, then Tim fucked 14.3% of the girls who got fucked by one of them. But what if Tim fucked 2 girls?

Triple posting because this example is awesome.

I was thinking about the range of girls I've had sex with, and let's say it was five brunette combos, two blonde combos and one redhead combo. Now what if I fucked twice as many blondes?

Originally Posted by spoonitnow

It's not really, but the average person's understanding of what "twice as often" means gets screwed up when you start talking about percentages, which is part of the point of the thread.

If Bob fucked 6 girls, and Tim fucked 1 girl, then Tim fucked 14.3% of the girls who got fucked by one of them. But what if Tim fucked 2 girls?

Originally Posted by spoonitnow

Triple posting because this example is awesome.

I was thinking about the range of girls I've had sex with, and let's say it was five brunette combos, two blonde combos and one redhead combo. Now what if I fucked twice as many blondes?

Spoon is a natural teacher I'm telling ya!

So yeah I was going to post moar and make my point etc but seriously, what kind of a douche would I look like if I disagreed with spoon? I've decided instead to post the following picture. I believe this is a wise choice.

Originally Posted by Penneywize

So yeah I was going to post moar and make my point etc but seriously, what kind of a douche would I look like if I disagreed with spoon? I've decided instead to post the following picture. I believe this is a wise choice.

There's nothing wrong with disagreeing with me.

Imagine the same question as the OP except you have 60% equity against his range. If he doubles his bluffing frequency, you can't have 120% equity.

Man spoon I am really doing my best here. I would argue with you if I saw a point, but I'd be arguing about language and not so much poker; and hey, this is your thread so I'm auto-wrong anyway aren't I? :P

I could pm you if you really wanted to hear more about this but I doubt it would accomplish much.

Originally Posted by Penneywize

Man spoon I am really doing my best here. I would argue with you if I saw a point, but I'd be arguing about language and not so much poker; and hey, this is your thread so I'm auto-wrong anyway aren't I? :P

I could pm you if you really wanted to hear more about this but I doubt it would accomplish much.

You're heads-up in position on the river with a bluff catcher. Your opponent goes all-in with a polarized range of nut hands and bluffs.

Suppose you have 60% equity against his range.

How much equity would you have if he bluffed twice as often as he does now?

^^^= 75% equity (answer in white)

Just wanted to type this out as an easy to read post for those for whom it still might not be clear. Please ignore if you're ok with it already obvs.
The way I think of it:
Say villain's range has 7 strong hands which are the virtual nuts, and 3 that are bluffs, and he's shoving all of them. So our equity is 30% (3 hands/10), (because thats how often we win when we call with a medium strength hand).
In an alternative scenario he bluffs twice as often. So he now has 6 hands in his range which are bluffs, but he still has those 7 strong hands. So as we only beat bluffs, our equity is now 46% (6 hands/13).
Nothing more, just helping anyone who finds this sort of thing hard/confusing.

Originally Posted by spoonitnow

You're heads-up in position on the river with a bluff catcher. Your opponent goes all-in with a polarized range of nut hands and bluffs.

Suppose you have 60% equity against his range.

How much equity would you have if he bluffed twice as often as he does now?

72%

He bluffs 6 times, value bets 4 times

If he doubles his bluffing frequency, using the figure above he will then be bluffing 12 times and will still be value betting 4 times.

So for a total of 16 hands, 12/16 = 75%.

My first post by the way.

I think this needs clearing up for some people. Polarised does not mean balanced. Polarised means he can have good hands and crap hands, but not medium hands. Polarised does not mean anything to do with frequencies or equities. Polarised does not give us 50% equity.



e.g. AA, KK, AK, QQ, + trash is a polarised range. Whether or not it is balanced is entirely dependent on the number of combinations of trash hands in the range.


Penneywize you should really try to type out an answer to the 60% equity question. I think that will explain things for you.

Penneywize is arguing semantics, no biggie. I'm pretty sure he gets it though, at least I hope so.