Head Up Theory Question

[reubenf]

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

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Seems pretty damn likely.

[uphigh_downlow]

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This question is pretty much the infinite pot, infinite raise case treated in Part 3 of the [0,1] game. Answer is that you never fold, and that you bet/raise with top 41.4% of hands, reducing hand values with each additional raise.

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I guess i will have to read up more on this [0,1] game

It seems encouraging that the correct strategy is to bet/raise with top certain% hands.

I do believe that we can come up with such a number for pot-limit, since the pot odds are constant, but because this is a limit question, the value 41.4 will have to be replaced by different %s at every step. Also this is not a infinite pot. Very rarely will a huge pot be created in this case if experts are playing. Yes not even with 999,999 against 1,000,000.

In addition if you meant infinite pot as in no folds, I disagree with that too.

Lets assume that you have limited your oppnents range to 999,998, and 1,000,000, and its ok for you to raise. You raise and he reraises, it might be acceptable to fold. Or if his range is [999,998.5-1,000,000] Well obviously he has you beat.

I think in the finite possible holdings case, the entire objective might be to make someone fold eventually. I can see calling as a option in certain circumstances, but i suspect that quite a few games would end in folding.

if that encourages omeone to bluff, then all you have to do is exploit his bluffing, by calling/raising appropriately.

[donkey69]

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

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The Ante is $1.Therefore if you rank the cards against the ante 2 is worth $2 and 3 is worth $3. $1 is the unit against which all the other cards can be ranked.

[reubenf]

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

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The Ante is $1.Therefore if you rank the cards against the ante 2 is worth $2 and 3 is worth $3. $1 is the unit against which all the other cards can be ranked.

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It's very strange to say 2 is with $2. The only hand you can beat is a 1, and even then it would be difficult to win $2.

[mscags]

I'm getting all my money in

[Jefzter]

Heh! I’m seeing answers raising from 8 times to 70 times. Way to conservative in my view. The way I see it even if you get $1,000,000 in the pot your just only going to lose one in a million times! And you only want to raise 8, 20 or just 70 times at only $1 a time? Please sit at my table when playing no limit !!!

Instead of thinking about bluffing and pot odds, start thinking implied odds and how much you would bet knowing that you can only lose 1 out off 999,999 times.

I’m not sure if I would stop after one billion raises with the idea that I might lose 1% of the time.

[IronUnkind]

I should like to note that I am operating under the assumption that if my "expert" opponent held the nuts that he would continue raising ad infinitum. I suppose there exists a theoretical point in time where it becomes more likely than not that my opponent holds card 1,000,000. But even if I were certain that he held that card, I would still continue raising in order to play to a draw. My opponent could, of course, end the pissing match by calling, but he would be making a mistake in terms of TFTOP.

[jediael]

Wow, this thread is full of misunderstood pot odds.

Also everyone who suggests folding is clearly out of there mind.

This question is not about pot odds, it is about having an equity edge on your raises.

Note: Others got it before me, I would just like to write down my thought process anyways

I am going to elaborate:
Both you and your opponent are rational.

You bet because your hand is better than 500k. Your opponent knows that you bet because your hand is better than 500k. Your opponent figures therefore that your hand is in the 501k-1000k range. Your opponents thus expects you to have a hand with an avg strenght of 750k. Thus a hand with strength > 875k qualifies for the 1st reraise.
We can induce from this the range of hands that qualify for a further reraise get four times as small each time.

If the range of hands gets smaller than 1 then we should not reraise anymore, because our 999,999 hand does not lie in thta range anymore.

The following equation needs to be considered:
R(n) = 1000k-[500k / 4^n]

R(0) is the minimum hand for which betting is profitable
R(1) is the minimum hand for which reraising 1 time is profitable
etc.

If we put R(n) = 999,999 and solve for n we get: 4^n = 500k which comes down to n ~ 9.46

So one should reraise 9 times and then start calling.

[slimeywater]

You should fold
go home and enjoy the rest of your life with your unlimited bankroll

[ggbman]

I cannot fathom that the coeect answer is as low as some poeple are suggesting, i can't see how the number is in the single digits.