Bayes on Big Bluffs

[DukeOfDeath]

It's been awhile since I've written a strategy thread since I've been in med school. Yet it's med school itself that inspired this thread. Basically it's Bayesian Analysis. You can look it up if you're interested, but I won't bore you with details otherwise. Basically it's a way to calculate odds when things aren't black and white.

Here's an example: everyone knows the odds of rolling a 1 on a die: 1/6. But say you are at a casino where you can't see the die, and eveytime an odd number gets rolled there's a 50% chance a velociraptor drops from the ceiling and does a dance. Everytime the dealer rolls the die and a velociraptor doesn't appear, would you still guess that it's a 1/6 chance for a 1? If you're answer is yes, consider a 99.9% chance that a velociraptor comes on a 1.... seems quite slim that a roll with no dino dance would be anything but an even number now.

Why does this matter?: Well a lot of times people are at risk for genetic diseases or are having children that are at risk and so they need genetic counseling. I had only heard mathematicians and poker players using Bayesian before, but it's a big thing in genetics. A lot of genetic diseases are either 1/2 or 1/4 chance of being passed on. But it makes a world of difference to a patient to use other info in calculating the odds and be able to put the odds closer to 1 and better prepare them, or better yet putting the odds closer to 0 gives a lot of comfort to the patient.

OK OK OK, but what does this have to do with POKER...???: The straight up odds in this case are easy. For any 2 card hand there are 52 possible cards for the first and 51 left for the second, so 52X51 is a 2652 different starting hands. For pocket AA we do something similar: 4X3 is 12 different AA hand. And 12/2652 = a 1 in 221 chance of being dealt AA preflop. Now it gets trickier when you are guessing based on how people bet.

Let's say it's heads up on the river and you're faced with an all in decision to a guy that only bluffs <1% of the time. The board is A74 8 4 with no flush possible and you have 65. However you're almost-never-bluff opponent has definitely repped AA. In a tournament on the bubble where you'll be all in, it's hard (and most likely incorrect) not to fold, but if you have your opponent covered (or it's a cash game) it's technically wrong to fold.

I won't put the math here (although it's not THAT crazy if someone wants to see it), but I wouldn't be surprised if no one believed this without the math. I know it seems ridiculous to me at least, but when you think about it it kind of makes sense. If AA is 1/221 (actually 1/442 or half as likely with an A on the board giving him less possible AA) and he's bluffing 1/100 would it not be MORE likely that he/she's bluffing than having the nuts?

Disclaimer: As with all math based approaches to poker you should be careful when excluding the human factor. I think math based is the best approach still, but it should be the foundation only. You still need to go beyond the math and realize there are many circumstances that you can't reasonably put into a formula.

Basically this example shows that if your opponent bluffs more often than is dealt the nuts you should call with decent odds. However, you have to realize that if your opponent is getting a lot of calls or betting from you (especially if they are as tight as <1% bluff) it's highly unlikely they will use their 1/100 bluff in this spot. But also you have to realize that on this site there are players who are tight, but also don't put YOU on a hand well. So you can easily find a player who's even tighter than 1% bluff but can accidentally turn a made hand into a bluff by thinking they are unbeatable with AK, A8, A7 for two pair or a 4 for three of a kind.

So basically this can help you start thinking outside the box when making tougher decisions, as long as you keep in mind that it's always complex. And above all don't get results oriented. Just like you don't start folding KK preflop because of the one time CaptainSandy has AA and beats you ( ), you also shouldn't give up a mathematically correct play because of the times it doesn't work. Likewise if you call down a bluff once, it's easy to see all you win and feel like calling down EVERY river. Let's just say that's not always best.

Anyway, hope this was helpful for at least one person out there. If anyone wants a crash course in Bayesian, or my calculations if you already are familiar, or just a philisophical discussion on parallel universes lol then I can PM you. For the rest you can skim the surface and hopefully still get something out of it, consider yourself rewarded for reading this far. And of course if I'm wrong anywhere please let me know.

See ya at the tables

[DreamALot]

D'oh! Now I get it!!!!

[DukeOfDeath]

Originally Posted by DreamALot

D'oh! Now I get it!!!!

haha. homer simpson equals best river player ever lol

[T_B_H]

nice thread

if u r gonna play real money its essential you understand how to calculate odds and play accordingly, theres no harm in loosing a hand to a better 1 as long as u played it right

for me odds/position/pot control(if u dont have the nuts) and hand reading are as important as the cards you are dealt

where always all learning at this game, but in real money you can pay dearly for bad calls/plays even gut feelings in a hand, sometime those pay off sometimes not

maximise ur winning and minimise ur losses and who wont go far wrong

[DukeOfDeath]

Yeah I think it's very important to learn to make tough river calls (especially against someone you know can bluff). However, learning when to fold is almost MORE important.

Minimizing losses maximizing wins just like you said.

Too often I see people call any standard raise from me preflop and any bet less than pot on the flop or turn just to fold the river. It sucks that I don't get paid off my last bet when I have the nuts, but it also makes it way too easy to bluff too. You're basically building a bigger pot for someone to steal from you on the river.