I Know 2+2 Wants To Kill Me For This......

[StellarWind]

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I'm a little confused. I guess we're assuming that we can't tell anything from the cards we're dealt?

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Correct, you cannot predict who will flop TPTK based on your preflop cards. Assume you cannot see your hand preflop.

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If we're not allowed to see our cards until after the flop, then it doesn't matter because this would be a complete coin toss every time.

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Correct. These are straight even bets on a 50-50 chance. They have zero EV. Bet and raise if you enjoy gambling.

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The idea here is to keep the pot as small as possible at either 0 or 1 bets. In other words, we check or we call. This allows our "gambling" opponent to make the biggest mistake on the flop by peeling when he has the gutter.

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Suppose Villain bets preflop. You can call this bet or you can raise in which case assume Villain will call.

Thus the preflop pot can be 2 SB or 4 SB at your option. The preflop raise carries zero EV.

Now consider the postflop play. A gutshot should be folded on the flop irrespective of whether the pot is 2 SB or 4 SB. Hero will play the hand exactly the same postflop regardless of what he did preflop. For his own reasons Villain will also play the hand exactly the same postflop.

Since the postflop action will be identical in every respect, it follows that the preflop action cannot change the winner of the pot nor the amount of postflop bets won by the winner. We also noted above that the preflop raise has zero EV.

So why do you think it is more profitable not to raise preflop? If the bigger Sklansky mistake means you make more money, then where is the extra money coming from? It's not preflop and it's not postflop either.

There is a way out of this apparent paradox. The Fundamental Theorem is not wrong.

[waffle]

hi stellar,

does it have to do with the idea that all of the PF equity is not realized because the chaser does not get to see all 5 cards?

edit: or is it something to do with not knowing if we'll flop tptk or the gutshot when we raise pf?

or does it have to do with a donation of .5 bb that i make when the gutshot hits post?

this paradox is really confusing me and it disturbs me how uncomfortable i am thinking out this bit of theory. [img]/images/graemlins/crazy.gif[/img]

[Guruman]

It looks like I misunderstood your premise a little there Stellar. I'll take another whack.

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Suppose Villain bets preflop. You can call this bet or you can raise in which case assume Villain will call.

Thus the preflop pot can be 2 SB or 4 SB at your option. The preflop raise carries zero EV.

Now consider the postflop play. A gutshot should be folded on the flop irrespective of whether the pot is 2 SB or 4 SB. Hero will play the hand exactly the same postflop regardless of what he did preflop. For his own reasons Villain will also play the hand exactly the same postflop.

Since the postflop action will be identical in every respect, it follows that the preflop action cannot change the winner of the pot nor the amount of postflop bets won by the winner. We also noted above that the preflop raise has zero EV.

So why do you think it is more profitable not to raise preflop? If the bigger Sklansky mistake means you make more money, then where is the extra money coming from? It's not preflop and it's not postflop either.

There is a way out of this apparent paradox. The Fundamental Theorem is not wrong.

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I think that there is no edge one way or the other when both players consider the odds. regardless of the size of the pot, the one who flops top kicker will automatically take down the pot uncontested.

With the gambler, the edge has to come from position, but only because this hand will be won on the turn every time.

I think a critical question is, what will top pair do on the turn those times that the gutshot connects?

will he recognize the straight board and opt to check/fold?
will he bet if he is checked to?
will a made gutshot lead every turn?
if a made gutshot checkraises, will the top pair pay him off?

I can’t figure this one without accounting for the turn here.

[Guruman]

--also, I made an assumption on the position of the button and the blind structure. Having the BB become the dealer seems like it would be significant.

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There is a way out of this apparent paradox. The Fundamental Theorem is not wrong.

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I don't see much of a paradox in this example. It's fairly simple:

The only place we make money is from his flop call when he's the one with the gutshot. But, we don't make ALL of his flop call, because sometimes he will complete his gutshot allowing him a discount on his loss. The smaller the pot is at that point, the smaller the discount he gets. When he makes less the times he hits, we make more.