Calculating Odds at the Table

[Bill Kolter]

Help me out here. I'm learning Hold'em, and I have a pretty good handle on how to calculate outs vs. pot odds. But I'm having a hard time
putting players on hands and calculating whether I'm an underdog.

Here's an example from the WPT. Chip Reese, Barry Greenstein, and an amateur named James Tippin were playing. Reese had K-6, Greenstein A-K, and Tippin Q-Q, and all three were all-in.

The TV screen indicated that Tippin was favored 50-33-17.

So I ask, "How do I figure this at the table on the fly?"

I suppose, if I'm Tippin, I first have to guess what my opponents have. Then I have to figure the odds of Greenstein catching an ace or a king (or an ace AND a king, or two aces, or two kings, etc.) vs. the odds of Reese catching 2 sixes vs. the odds of Tippin NOT catching a queen, and then comparing that to the payoff. Then again, maybe this "underdog" calculation takes into account the odds of everybody improving. I don't know, but it gives me a headache.


Or I can just look at the queens and go, "How pretty. I call." Tippin busted out, by the way, when Greenstein caught an ace AND a king, but according to the math, he made a good call. At least, that's what Vince Van Patten thought. I'm pretty sure I wouldn't lay down queens in that situation.

Can anybody help me out here? This "underdog-overdog" thing is driving me nuts. Figuring my odds of hitting a hand is easy. Figuring against an opponent seems a lot tougher, and against two opponents, I'll need Microsoft Excel. What is the proper method to calculate this?

[That guy]

its much tougher than that even...

the best way to do this (and what most mathematically oriented pros like Lederer, Gus Hansen etc do) is select a 'range of hands' for each opponent and then estimate a weighted average of all the scenarios. This is obviously very complicated but in reality, most of these match ups are similar and after many years of doing this, they can come up with a reasonable estimate.

in this case, there was a bunch of money in the pot... anytime there is money in the pot and you estimate your chances of being 50%, it is mathematically correct to call.

the only hands that Tippin is not at least 50% to win is if Greenstein or Reese has AA or KK. So the question really comes down to that -- are you looking at AA/KK or is there a good chance Greenstein has something other than AA or KK.

Mike Sexton later wrote in an article that there are only 3 hands Greenstein would move all-in with: AA KK or AK. Sexton argued that Tippin should have folded given that at best he was 55% favorite (vs AK) but there was a good chance that Greenstein had AA or KK, in which case Tippin is only 20% to win the pot and he shouldn't call, even with a bunch of money in the pot.

Mathematically, if you are Tippin you could argue that there are 6 ways each to make AA and KK (since you don't hold an A or a K) and 16 ways to make AK, you could say that it is 16 to 12 (4:3) likelihood that Greenstein holds AK and not AA or KK.

so out of 28 combinations, Tippin is:
20% to win the pot 43% of the time
55% to win the pot 57% of the time
(.2x.43)+(.55*.57)= .086+.3135 = ~40%

Tippin is therefore 40% to win on a blended basis using these assumptions and needs ~1.5 pot odds to make the call correct...

That was an interesting hand. Sexton asked Barry if he would have called if Tippin had gone all-in and not just called Reese's bet... Barry said he would have folded if Tippin had gone all-in...

[Bill Kolter]

Yikes! That's gonna hurt my noggin. Great response, though. It clarifies the situation quite a bit.

Thanks.

[Token]

[ QUOTE ]
there are 6 ways each to make AA and KK

[/ QUOTE ]

What does this mean?

[Guruman]

6 ways to make AA:

A /images/graemlins/spade.gif,A /images/graemlins/diamond.gif
A /images/graemlins/spade.gif,A /images/graemlins/heart.gif
A /images/graemlins/spade.gif,A /images/graemlins/club.gif
A /images/graemlins/diamond.gif,A /images/graemlins/heart.gif
A /images/graemlins/diamond.gif,A /images/graemlins/club.gif
A /images/graemlins/heart.gif,A /images/graemlins/club.gif

The same suit combinations are available for KK.
/images/graemlins/smile.gif

[Token]

I see. Thanks.

[Sean_A]

Thanks for the post.

[ QUOTE ]
so out of 28 combinations, Tippin is:
20% to win the pot 43% of the time
55% to win the pot 57% of the time
(.2x.43)+(.55*.57)= .086+.3135 = ~40%

[/ QUOTE ]

Under what conditions, Ax and Kx hands figure out into calculation of odds?

[elmitchbo]

this is partially just a bump post to get some more interest. i have the same problem. i made a post about a similar thing.
http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1693999&page=2&view=c ollapsed&sb=5&o=14&fpart=1

i'm still trying to figure out how to put a hand range on someone and apply that to my outs or their outs or whatever you have to do to know what's the best thing to do. the more replies to this the better.