TajProfessor: Optimal Betting Curve (is John Turmel a nut?)

[Zim]

Anyone want to try to explain this post to me?

-----------------------------------------------------

How do we get a copy of your fourth year engineering
project?

JCT: It's never been published.
21 Pages of print-out and math.
But you can figure out the optimal betting curve
by figuring out fair odds given 5% edge, 52.5%:47.5%

The equation is Bet=[q/(p-q)] where p=winner's chance
and q= loser's chance.

For 10% edge, it's 55:45 so Bet=[.45/(.55-.45)] = .45/.1 =
4.5 BETS Bet more and opponent must fold or take bad odds.

For 20%, it's 60:40 so Bet=[.4/(.6-.4)] = .4/.2 = 2 BETS
Bet more and opponent must fold or take bad odds.

For 50%, it's 75:25 so Bet=[.25/(.75-.25)] = .25/.5 = 1/2
BET Bet more and opponent must fold or take bad odds.

For 100%, it's 100:0 so Bet=[0/1] = 0 BET
With no chance of losing, anything you can get out of him is
too much when, given no chance of winning, he should never
call.

It's counter intuitive to what most people think.
The smaller your edge, the more you must bet to protect.
The larger your edge, the less you must bet.
But you must never give opponent a positive call.
You'll rarely get an overlay when calling me except
in limit games where they're often available which is
why the Turmel2Step is necessary to automatically
highlight the winners and the losers for your choice.
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JCT: This is extraordinarily important in no-limit poker.
But to think that you have to bet 4.5 times the size of the
pot when you only have a 10% edge goes against most people
feeling more comfortable betting big with big edges. But big
edges don't need to big bets like small ones do. So you can
imagine what a maniac a player who understands that he has
to put it all in on small edges would seem to the others.

I can say for certain but it sounds like the kind of play
Doyle Brunson was famous for. Putting it in over and over
again on small edges. Now you know why it made him a winner
to have kept pushing out the draws. And if they finally
called, they were often getting bad odds. And when they
caught him, he still had his outs.

You have to bet big with small edges like you can bet small
with big ones. Very counter-intuitive.

http://games.groups.yahoo.com/group/...tep/message/14

--
John C. "The Banking Systems Engineer" Turmel, Author of the UNILETS
interest-free time-based currency United Nations C6 recommendation to
Governments in the http://www.un.org/millennium/declaration.htm
http://www.cyberclass.net/turmel / http://www.medpot.net 613.632.2334

[pzhon]

IIRC, Turmel was a borderline crackpot in other contexts. He proclaimed that control of the world financial systems should be turned over to engineers because engineers understand feedback systems, or something like that. It's interesting to see him turn his "insights" to poker theory.

The idea he points out is that if you know your edge is small, and your opponent knows your edge is small, it takes an overbet to force your opponent out.

In practice, you don't know exactly what your edge is. If you overbet with what you think is a small edge, say with 55 against overcards, you will get called when you were horribly wrong, and the cost of this is prohibitive.

You also have to take into account implied odds and bluffing.

I think it is better to imagine a market whose consumers are the different hands your opponent could have, weighted by likelihood. As a simple approximation, if there can be no raises, and no betting on future streets, then each hand may have a maximum amount it is willing to call. If you bet too much, only the strong hands will call, and you may lose more from those times than you gain from buying many pots. If you bet too little, you will get called by more hands, but you might leave too much money on the table. The profit-maximizing bet sizes depend on the distribution of calling thresholds.

[Cerril]

Some things are relevant, but for the most part he seems to ignore that poker is a game of incomplete information (I feel like that phrase should be trademarked, but I'll use it anyway, cliche` or no). If you know something is the case and you also know your opponent knows something is the case, and your opponent plays rationally then that sort of betting strategy has some merit - obviously if you'll get called with a worse hand 0% of the time and your opponent will check behind 100% of the time, then betting is pointless.

But yes, he does forget about all those things that involve your opponent not seeing your cards, and you not knowing exactly what they hold.