Quote:DobrijHi 2 ALL !

I apologize if this question has been raised before, if yes please link me.

The QUESTION:

How much advantage the gambler gets if in UTH before opens flop, will know with a probability ~33%, one of the cards

?!?

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Unfortunately, I did not analyze the situation of knowing one Flop card and no Dealer cards. My results are here:

https://advancedadvantageplay.com/novelty-games/

And downloads for UTH here:

https://advancedadvantageplay.com/downloads/

Quote:HunterhillI was going from memory, I just found it. If you know one flop card you have a 3.6 % edge on that hand. So if you’re only getting it 33% around 1.2 %Quote:DobrijQuote:Hunterhill

In that case I think you will have around a .75-1% edge

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Is this a total end hand advantage EV = +1%? Or additional to the optimal -2% + 1% = -1%?

How did you calculate it, or did you take it out of your head?

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It’s in CAA

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Maybe I’m overthinking this…. But you are defining the edge when he is correct that 33% of the time. Are you also including the worse EV when he makes decisions based on incorrect information 67% of the time?

Quote:SOOPOOQuote:HunterhillI was going from memory, I just found it. If you know one flop card you have a 3.6 % edge on that hand. So if you’re only getting it 33% around 1.2 %Quote:DobrijQuote:Hunterhill

In that case I think you will have around a .75-1% edge

link to original post

Is this a total end hand advantage EV = +1%? Or additional to the optimal -2% + 1% = -1%?

How did you calculate it, or did you take it out of your head?

link to original post

It’s in CAA

link to original post

Maybe I’m overthinking this…. But you are defining the edge when he is correct that 33% of the time. Are you also including the worse EV when he makes decisions based on incorrect information 67% of the time?

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I had understood that he sees the bottom card 1/3 of the time. When he makes a decision he knows whether or not he has seen the card. So he never makes a non-optimal decision.

I have a different issue on the calculation. Seems like it is just dividing the player edge of 3.6% when you see a card by 3. I would have thought you instead need to weight 3.6% 1/3 of the time and the negative edge of UTH 2/3 of the time to get an overall edge for this game.

Quote:unJonQuote:SOOPOOQuote:HunterhillI was going from memory, I just found it. If you know one flop card you have a 3.6 % edge on that hand. So if you’re only getting it 33% around 1.2 %Quote:DobrijQuote:Hunterhill

In that case I think you will have around a .75-1% edge

link to original post

Is this a total end hand advantage EV = +1%? Or additional to the optimal -2% + 1% = -1%?

How did you calculate it, or did you take it out of your head?

link to original post

It’s in CAA

link to original post

Maybe I’m overthinking this…. But you are defining the edge when he is correct that 33% of the time. Are you also including the worse EV when he makes decisions based on incorrect information 67% of the time?

link to original post

I had understood that he sees the bottom card 1/3 of the time. When he makes a decision he knows whether or not he has seen the card. So he never makes a non-optimal decision.

I have a different issue on the calculation. Seems like it is just dividing the player edge of 3.6% when you see a card by 3. I would have thought you instead need to weight 3.6% 1/3 of the time and the negative edge of UTH 2/3 of the time to get an overall edge for this game.

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I agree with what UnJon said. Given the EoR of the two hands where we assume we do not know one of the flop cards (which, even with Optimal Strategy, only impacts the first decision point anyway) I would say that the overall advantage on the game is razor-thin. Roughly 0.15% if we assume that the 3.6%/3 = 1.2% is right for those hands where we do have an advantage.

If you were to play 3 hands assuming you are betting $100 per hand you would lose 2.36 x 2 is 4.72

Then on third hand you see it and win 3.60 so you are losing 1.12 over 3 hands.

Am I thinking about this in the wrong way?

Quote:HunterhillOn second thought I’m not sure you would have any edge.

If you were to play 3 hands assuming you are betting $100 per hand you would lose 2.36 x 2 is 4.72

Then on third hand you see it and win 3.60 so you are losing 1.12 over 3 hands.

Am I thinking about this in the wrong way?

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I believe so, though I could be wrong. That's why I used EoR, as opposed to House Edge. I had assumed the 3.6% edge was on all monies bet (similar to EoR) as opposed to just the initial bet. That makes sense to me because most of the realized value comes from either making, or not making, the 4x bet when you otherwise either would or would not. If this decision is unchanged either way, then seeing the flop card in advance did not help you that hand.

What’s important is, what strategy variation should we use when one flop card is accidentally exposed? That determines the house edge.

Quote:acesideThis is the gambling world, so the convention is to leave the conclusion as vague as possible. The 3.6% house edge should be referenced to the ante bet amount only, I guess, because the Wizard’s house edge number of 2.2% is referenced to it. We can also reference it to the total initial bet of that hand, which will decrease house edge a lot.

What’s important is, what strategy variation should we use when one flop card is accidentally exposed? That determines the house edge.

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In terms of what's known; I would assume that if the one exposed card would lead you to making the 2x Raise (as if we didn't know it), then we should make the 4x Raise instead. In that instance, it would apply only to making the 4x Raise if the known flop card would give you a pair with one of the cards in your hand. The four flush and two pair would not apply, because we couldn't know that we will end up with those.

That aside, I think someone would have to know how to put together a program to figure it out. I suppose it would be possible to figure out every possibility on what would otherwise be borderline 4x Raise decisions by hand, but it would sure take awhile. This calculator on WoO:

https://wizardofodds.com/games/ultimate-texas-hold-em/calculator/

I would think, could theoretically be modified to calculate for a known card. As the calculator is now, with an extremely borderline hand such as K2 or K3 suited, (especially K2) we see that the value compared to checking is not that great of a difference. If I had to guess, I would say that just knowing one of the cards is NOT in the suit you have would be enough to check instead. I would also suppose that something like J7 suited would become a Raise if you know that at least one of the flop cards are of that suit.

Something like J9 off might become a Raise if you know the card coming out is lower than a nine, but I'm not sure.

Anyway, I assume the Player Edge proposed came from somewhere (CAA, I see), so I'd assume that the strategy must be known in arriving at that number.