UTH, one flop card

Hi 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
?!?

I guess Dr Eliot has researched this. He is here. However, I believe you will get a lot more advantage if you know any information about the dealer’s hole cards.

Quote: aceside

I guess Dr Eliot has researched this. He is here. However, I believe you will get a lot more advantage if you know any information about the dealer’s hole cards.
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At the moment there is only information one of 3 flop cards. Do you have info about advantage
?!?

I don’t know but can estimate it. This little information should easily flip the house edge to the favor of the player.

Quote: Dobrij

Quote: aceside

I guess Dr Eliot has researched this. He is here. However, I believe you will get a lot more advantage if you know any information about the dealer’s hole cards.
link to original post

At the moment there is only information one of 3 flop cards. Do you have info about advantage
?!?
link to original post

I believe it’s in the 3% range

Quote: Dobrij

Hi 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
?!?
link to original post

33% chance to know rank AND suit or just rank? Meaning you think it is the 5 of spades and it will be the 5 of spades 33% of the time, but it is just as likely to be the 5 of clubs or the 9 of diamonds? In the real world if you can glimpse a card you are not likely to confuse a jack with a 6, but more likely to confuse a jack with a king.

Quote: SOOPOO

Quote: Dobrij

Hi 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
?!?
link to original post

33% chance to know rank AND suit or just rank? Meaning you think it is the 5 of spades and it will be the 5 of spades 33% of the time, but it is just as likely to be the 5 of clubs or the 9 of diamonds? In the real world if you can glimpse a card you are not likely to confuse a jack with a 6, but more likely to confuse a jack with a king.
link to original post

In 33% of cases I will know a specific card, face value and suit

Quote: Dobrij

Quote: SOOPOO

Quote: Dobrij

Hi 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
?!?
link to original post

33% chance to know rank AND suit or just rank? Meaning you think it is the 5 of spades and it will be the 5 of spades 33% of the time, but it is just as likely to be the 5 of clubs or the 9 of diamonds? In the real world if you can glimpse a card you are not likely to confuse a jack with a 6, but more likely to confuse a jack with a king.
link to original post

In 33% of cases I will know a specific card, face value and suit
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In that case I think you will have around a .75-1% edge

Quote: 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?

Quote: Dobrij

Quote: 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

I 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 %
It’s in CAA

Quote: Dobrij

Hi 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
?!?
link to original post

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: Hunterhill

Quote: Dobrij

Quote: 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

I 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 %
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?

Quote: SOOPOO

Quote: Hunterhill

Quote: Dobrij

Quote: 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

I 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 %
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.

Quote: unJon

Quote: SOOPOO

Quote: Hunterhill

Quote: Dobrij

Quote: 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

I 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 %
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.
link to original post

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.

Yes I agree with this also.

On 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?

Quote: Hunterhill

On 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?
link to original post

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.

This 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.

Quote: aceside

This 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.

Wonderful work! Based on what you say, I guess this is the key strategy: “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.”