Head Up Theory Question

[uphigh_downlow]

You are certainly right. My reply was hasty and not well thought out.

So if the pot is 20 million, it is certainly never right for you to fold to a $1 bet.
So it is certainly not ok for anyone to bet, but for value.
Any fold would be catastrophic. A bluff bet would be -EV. But I do understand the circular logic that you are trying to point out.

In this case Xo would be ~50%

It seems that you would raise for value fewer number of times, and the raising range would be halved everytime.

So it seems to me now that most of the people that have suggested halving the range at every raise, actually are dealing with big pot sizes, which were created as a result of either antes, or previous raises. As a result subsequent raises dont alter the pot-odds significantly

However, for smaller starting pots, its ok to open with worse hands and consequently raise with wore hands.
In the given problem I think its ok to open with a certain top % of your hands. I believ that this number lies between 50% and 75%. BUt what it exactly is, I do not know yet. After every raise, this numner tends further towards 50%.


It seems to me that for pot-limit, this number would be constant, since the pot always offers the same odds.

I'm trying to locate a mathematica cd. That should solve it for me.

At the moment it seems from these boundary conditions that the number of times you should open the pot is between 18 and 45.

[silkyslim]

catlover, i dont see how u win 0 bets instead of one if u raise and your opponents fold. plz explain

[MicroBob]

[ QUOTE ]
So if the pot is 20 million, it is certainly never right for you to fold to a $1 bet.
So it is certainly not ok for anyone to bet, but for value.

[/ QUOTE ]


......so if I am holding card #3 and my opponent bets I can almost DEFINITELY fold because I know that my opponent will ONLY be betting for value....
and then my opponent KNOWS that I KNOW this....so when he holds card #2 he will almost DEFINITELY bet because he knows that I might fold an inferior hand because I KNOW that he will not be bluffing....


and around and around we go.


If he knows that we are assuming that the ONLY betting that can take place is for value then that just makes the case for bluffing at it with total garbage more legitimate doesn't it?

[MicroBob]

[ QUOTE ]
This is getting almost cruel watching peope trying to develop game theory from scratch.

[/ QUOTE ]



I'm happy to provide you, David, and others with all the car-crash-onlooker entertainment you can handle.

I aim to please.

[IronUnkind]

Nice rebuttal. If my opponent just calls me with the nuts, which one of us has made the mistake?

[M.B.E.]

[ QUOTE ]
I am pretty sure that the game-theoretic strategy never bluffs when the pot is this big, since your opponent will call every time.

[/ QUOTE ]
In theory you would have to bluff sometimes but very very rarely.

Pot starts out at $20-million and the initial bet is $1. I'm not saying you should bluff every time you are dealt card 1. (That would be a 0.0001% bluffing percentage.) It would be enough to bluff 2.5% of the time you are dealt card 1. (A 0.0000025% bluffing percentage.)

That way suppose your opponent is dealt card 2. Your opponent knows that you are betting for value with the top 41.4% of your hands, and bluffing with 0.0000025% of your hands. So if you do bet, the probability you are bluffing is:

0.0000025/41.4000025
=1/17-million approximately

That forces your opponent to call with card 2 (and higher), since the pot odds are 20,000,001:1. That way you will get paid off when you valuebet your legit hands.

Getting back to the original game posed by David in this thread: even after nine or ten bets have gone in, it's incorrect to say that the players are never bluffing. At that stage there would still be a tiny chance that at least one of the players is bluffing.

[Yeti]

I don't have a clue what the answer is, nor do I have any idea how to work it out.

Purely guessing, I'd imagine it's somewhere around 70. I eagerly await the results.

[reubenf]

Just curious, why do you call it Fair Value Betting?

[uphigh_downlow]

[ QUOTE ]
[ QUOTE ]
So if the pot is 20 million, it is certainly never right for you to fold to a $1 bet.
So it is certainly not ok for anyone to bet, but for value.

[/ QUOTE ]


......so if I am holding card #3 and my opponent bets I can almost DEFINITELY fold because I know that my opponent will ONLY be betting for value....
and then my opponent KNOWS that I KNOW this....so when he holds card #2 he will almost DEFINITELY bet because he knows that I might fold an inferior hand because I KNOW that he will not be bluffing....


and around and around we go.


If he knows that we are assuming that the ONLY betting that can take place is for value then that just makes the case for bluffing at it with total garbage more legitimate doesn't it?

[/ QUOTE ]

I think the point is that if you actually fold, the opponent will pick up on this, and he can increase his equity, by betting slightly more than top ~50% of his hands, depending on your folding frequency

So he can exploit you. So you basically never fold, to give him that edge.

As you can well imagine, a singlle bad fold is a catastrophic mistake.

if one player has the edge in this game because of position, then there is nothing anyone can do about it.

[uphigh_downlow]

[ QUOTE ]
[ QUOTE ]
I am pretty sure that the game-theoretic strategy never bluffs when the pot is this big, since your opponent will call every time.

[/ QUOTE ]
In theory you would have to bluff sometimes but very very rarely.


[/ QUOTE ]

Well its hard to define bluffing in this case. Are you trying to say that you should bet with your worst hands. That seems quite counter intuitive to me(although it might be well worth exploring). To me it means betting with slightly worse than the average value of the cards in play. This is just because of the fold equity. It would seem that if we used rational numbers(there are infinite rationals) on the cards, theoretically you would always have some Fold Equity, but with the finite set that we are dealing with here, I think the FE would converge to 0 at some point.

In my strategy, I do accept that you might fold to a raise with the bottom X/p+1 % of the opponents possible holdings. The folding equity is inversely proportional to the size of the pot.


I'm going to try and see how raising with bottom b% and top t% hands play out in this case. That should be a good indication if bluffing with worst hands is actually profitable