UTH "change in EV" questions

Hi, I noticed dealer errors the last few months playing UTH (Ultimate Texas Holdem) and was wondering what the advantage would be for the following, assuming "it happened every applicable hand" (see table below):

Situation	Advantage
Miss Pays:
Paid ante on ALL wining hands
Paid 3/1 on the blind bet for a flush
Paid 1/1 blind bet, with less than a straight
Paid on a dealer flush ###(player has losing hand)
***
"Flashing dealer, one flop card" situations:
Can see the card perfectly
Can only see color, and if it is a picture card or not

###: Two dealer pocket flush cards , and all combos of exactly three community flush cards.

Cell ***: Means, same as ### above, except NOT miss-paid if the community cards are: FL-FL-FL-N-N, N-FL-FL-FL-N or N-N-FL-FL-FL

Note: FL = Flush Card, and N = not a flush card (so, all other suits).

----
Thanks in advance for any help

ksdjdj

Quote: ksdjdj

Hi, I noticed dealer errors the last few months playing UTH (Ultimate Texas Holdem) and was wondering what the advantage would be for the following, assuming "it happened every applicable hand" (see table below):

Situation	Advantage
Miss Pays:
Paid ante on ALL wining hands
Paid 3/1 on the blind bet for a flush
Paid 1/1 blind bet, with less than a straight
Paid on a dealer flush ###(player has losing hand)
***
"Flashing dealer, one flop card" situations:
Can see the card perfectly
Can only see color, and if it is a picture card or not

###: Two dealer pocket flush cards , and all combos of exactly three community flush cards.

Cell ***: Means, same as ### above, except NOT miss-paid if the community cards are: FL-FL-FL-N-N, N-FL-FL-FL-N or N-N-FL-FL-FL

Note: FL = Flush Card, and N = not a flush card (so, all other suits).

----
Thanks in advance for any help

ksdjdj
link to original post

Hello!

I'll tackle a few of these in a couple of hours. The top questions I should be able to answer whereas the bottom two I think I can find an article on hole-carding UTH that covers this information.

Quote: ksdjdj

Hi, I noticed dealer errors the last few months playing UTH (Ultimate Texas Holdem) and was wondering what the advantage would be for the following, assuming "it happened every applicable hand" (see table below):

Situation	Advantage
Miss Pays:
Paid ante on ALL wining hands
Paid 3/1 on the blind bet for a flush
Paid 1/1 blind bet, with less than a straight
Paid on a dealer flush ###(player has losing hand)
***
"Flashing dealer, one flop card" situations:
Can see the card perfectly
Can only see color, and if it is a picture card or not

###: Two dealer pocket flush cards , and all combos of exactly three community flush cards.

Cell ***: Means, same as ### above, except NOT miss-paid if the community cards are: FL-FL-FL-N-N, N-FL-FL-FL-N or N-N-FL-FL-FL

Note: FL = Flush Card, and N = not a flush card (so, all other suits).

----
Thanks in advance for any help

ksdjdj
link to original post

Paying Ante on ALL Winning Hands:

Okay, so the first thing that we have to do is determine what percentage of hands are winning, but would normally not have the ante paid on them. We can go here:

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

If we go down to the return table for the game, then what we want are hands where the player wins and the dealer does not qualify. These probabilities are given in the return table, so we would just add those together.

0.055972 + 0.002927 + 0.001829 + 0.000008 + 0.000003 + 0.038965 + 0.001620 + 0.001396 + 0.000013 + 0.025907 + 0.004890 + 0.001471 + 0.000010 = 0.135011

In other words, this results in an expected gain of 0.135011 units every hand.

We typically expect to wager 4.152252 and lose .02185, or 2.185% so that represents an expected loss of 0.0907267062 units.

Instead, we are going to gain an additional .135011 units, so when we subtract from that the .0907267062 units that we would normally expect to lose, we end up with an expected positive outcome of 0.0442842938 units, which reflects a player advantage of 0.0442842938/4.152252 = 0.01066512673 or 1.0665%.

One thing that is probably worth noting is that there may be a few strategy changes that would come about as a result of this, particularly when it comes to an unpaired (and, obviously not better than a pair) board on the final decision to call or fold. In this instance, the player might also win the ante bet even if the dealer does not qualify.

I remember thinking the advantage was much larger before...hopefully I was wrong then and am right now.***

Paying 3:1 on the Blind Bet for a Flush

We have the following probabilities for a Flush in this game:

0.008666 + 0.001829 + 0.005487 + 0.001396 + 0.006866 + 0.001471 = 0.025715

Okay, so that represents the total probability of all winning flushes.

Typically, the Blind Bet would pay 3:2 on a Flush, so for $5 units, this would be $7.50. Instead, you are getting paid at 3:1, which would be $15.

(.025715 * 3) - (.025715 * 3/2) = 0.0385725

With that, the expectation seems to be that we would gain an expected .0385725 units every hand.

Normally, we would expect to lose 0.0907267062 units every hand, so when we subtract our gains from that we end up with 0.0521542062 units that we would still expect to lose every hand. We expect to bet a total of 4.152252 units, so the House Edge becomes 0.0521542062/4.152252 = 0.01256046265

With that, it does reduce the House Edge to 1.256% and then you can divide by the expected total bet, in units, to get EoR if you like.

Paid 1/1 Blind Bet w/Less Than Straight

We're going to the Return Table again and this is just a function of how often does the player win with less than a straight.

0.055972 + 0.076036 + 0.131987 + 0.038965 + 0.049437 + 0.025907 = 0.378304

Once again, the expected units gained is the same as the probability because this pays us one unit that we would not otherwise be getting. With that, we take our normal expected loss, in units, of 0.0907267062 instead becomes an expected gain of 0.2875772938. With that:

0.2875772938/4.152252 = 0.06925815046 or a 6.9258% player advantage.

It's also important to note that this is not going to be exactly right as there would be strategy changes involved, as well. The player would fold significantly less often, but how much less often is above my pay grade.

Paid on a Dealer Flush

Paid what on a dealer Flush? Do you mean just the blind as if the player had the flush, or totally across the board paid as if the player had won the hand?

***I think I remember and the other question was the dealer always paying the Blind Bets, even if the dealer had won.

As far as the other stuff, Teliot handled most hole-carding UTH questions:

https://www.888casino.com/blog/novelty-games/ultimate-texas-holdem-hole-card-play-one-dealer-card-one-flop-card

Quote: Mission146

Quote: ksdjdj

Hi, I noticed dealer errors the last few months playing UTH (Ultimate Texas Holdem) and was wondering what the advantage would be for the following, assuming "it happened every applicable hand" (see table below):

Situation	Advantage
Miss Pays:
Paid ante on ALL wining hands
Paid 3/1 on the blind bet for a flush
Paid 1/1 blind bet, with less than a straight
Paid on a dealer flush ###(player has losing hand)
***
"Flashing dealer, one flop card" situations:
Can see the card perfectly
Can only see color, and if it is a picture card or not

###: Two dealer pocket flush cards , and all combos of exactly three community flush cards.

Cell ***: Means, same as ### above, except NOT miss-paid if the community cards are: FL-FL-FL-N-N, N-FL-FL-FL-N or N-N-FL-FL-FL

Note: FL = Flush Card, and N = not a flush card (so, all other suits).

----
Thanks in advance for any help

ksdjdj
link to original post

(snip)
Paid on a Dealer Flush

Paid what on a dealer Flush? Do you mean just the blind as if the player had the flush, or totally across the board paid as if the player had won the hand?

***I think I remember and the other question was the dealer always paying the Blind Bets, even if the dealer had won.
(snip)
link to original post

I guess it was a bit vague, if it is "easy enough" to do can you split it into two figures:

1) The dealer didn't think that they qualified .
2) Dealer thought they only qualified with a hand less than mine, eg "player two-pair vs dealer pair"


Thank you

Quote: ksdjdj

I guess it was a bit vague, if it is "easy enough" to do can you split it into two figures:

1) The dealer didn't think that they qualified (so only got the play bet)
2) Dealer thought they only qualified with two pair (or less)


Thank you
link to original post

(Quote clipped, relevance)

Am I to understand #1 to mean that the dealer paid the player as if the player had won because the dealer did not recognize that he had a flush?

For #2, you're saying that the dealer doesn't think he qualifies with trips or better?

1) Yes, the dealer thought he had nothing / didn't qualify.

2) Sorry about the wording, the only other times it has happened to me so far, are when the dealer's "next best hand" was a 2 pair or pair (where I had either a better pair or better two-pair, both times),

Quote: ksdjdj

1) Yes, the dealer thought he had nothing / didn't qualify.

2) Sorry about the wording, the only other times it has happened to me so far, are when the dealer's "next best hand" was a 2 pair or pair (where I had either a better pair or better two-pair, both times),
link to original post

Dealer Has a Flush, but We Do Not Lose

Okay, the first one is going to be a little tough. This is very much going to be an approximation.

The first thing that we have to look at is that I'm going to go down to, "Player Plays 4x Blind," and get the two probabilities for the player getting a flush, which is both with and without the dealer qualifying:

0.004696 + 0.021019 = 0.025715

In other words, this is the probability of the player getting any flush and winning, which is automatically also true of the dealer.

Obviously, if the dealer has a flush, then the dealer should have qualified, even if the dealer doesn't seem to think so. That being the case, the only results that are being flipped are ones in which the player has a flush, or worse, and loses to a dealer who qualifies with a flush.

The probability of the dealer qualifying and beating the player is:

0.141353 (Loss of Six Units) + 0.066196 (Loss of Four Units) + 0.097079 (Loss of Three Units)

I'm also not going to count folding because you just lose anyway, regardless if the dealer knows he has a flush, or not. Although, this might change the decision to call or fold against certain flush rich boards if perhaps you have a high(ish) card and there are four suited on the board; you'd no longer count the four-suited towards the 21 outs for the call/fold because the dealer doesn't know what a flush is.

Anyway, let's get our total expected loss from these. If it seems like it should be more, remember, we are only taking the losses in which the dealer qualifies, because he normally would with a flush. If the dealer did not qualify, then he did not have a flush anyway.

0.848116 + 0.264783 + 0.291238 = 1.404137 (Units)

Okay, so when the dealer qualifies and we lose, that represents a total of 1.404137 expected units lost.

The probability of the player (betting blind) having a Flush that is the superior hand should be the same as that for the dealer, so we multiply this by that probability:

0.025715 * 1.404137 = 0.03610738295

This reflects a swing of about 0.03610738295 units...but don't take that as gospel because I really just did the best I could with this one. My logic could be flawed somewhere. In any event, this would reflect an expected gain of .03610738295/4.152252 = 0.00869585539 or 0.869585539% Which is a swing of less than one percent and merely reduces the House Edge from 2.1850% to 1.31541446%****

Again, I could be off, so would appreciate any corrections. That said, this would impact only hands where the dealer would qualify anyway AND flushes are not that common, so it doesn't have a huge swing on anything.

When a flush beats another flush and the dealer's would have beaten the player's, but is treated as if the opposite happened, this also swings that the player will be paid for the Flush on the blind bet, as well, but it's an unlikely enough scenario (and is already accounted for on Ante/Play) that any change in EV from that, specifically, will be miniscule. I guess the same is true with dealer flush otherwise normally beating a player straight, but again, has already been accounted for on Ante + Play and is going to be a pretty negligible swing on the blind bet just because it happens so infrequently.

In general, I am going to OPINE that this alone would not be enough to create an advantage, even without accounting for what happens with the blinds when a dealer flush would otherwise normally beat an inferior player flush or a dealer flush would otherwise beat a player straight. I say opine because I didn't actually do it, but we know that the difference just on how the Blind bets are resolved is not going to be greater than what the Ante/Play bets have done as a result of not losing to dealer flushes.

I still don't quite get what #2 means, but if it relates back to when the dealer has a flush, I don't think the player winning including all situations in which the dealer has a flush and the player would have otherwise lost is, by itself, advantageous***. That being the case, the situation needing to be more specific than that would not be an advantage, either.

****Also, this assumes that the dealer would never just win some other way, which is not the case. For example:

Dealer: Ah, 8h

Board: Qh, 10h, 5h, Ac, 2d

Player: Qd Kd

Even if the dealer fails to recognize that he has a flush, the player still loses to a dealer pair of Aces v. a player's pair of Queens, so the fact that the dealer had a flush wasn't even needed for the player to still lose this hand. There is no quick way to account for all of these situations that I can think of, but suffice it to say, the dealer doesn't always need the flush that he has to beat the player, so the change in House Edge is not even as good as when we assume the player always wins this.

I had a session at NYNY with two really dumb dealers and a nearly as dumb pit boss. One dealer told me I could bet 4x AFTER the flop! I did so twice when having a pair (winning once) before the next dealer came in. On the hand I lost, I knew it was strong enough to bet the standard 2x but hesitated for a moment wondering whether it was also good enough for a 4x raise. I think the answer is that I should never hesitate to raise as large as possible when I have a raise-worthy hand.

Next dealer comes in, pays me on the ante even though she didn't qualify. Then she paid me as if I had won a hand even though I was outkicked. After paying out the last player on the table, she realized her mistake and called over the pit boss. The pit boss demanded I give back the two chips the dealer paid me. But she didn't ask me to give back the chips I should have lost. So I complied without saying anything. I don't think she was being generous. I think she was just dumb.

Another session I noticed a player making a 3x raise after the flop. Dealer paid him on his 3x bet. It was probably an honest mistake by the player who seemed new to the game. A player trying to sneak in an over-raise would likely go 4x while the dealer isn't looking to try to make it appear as though a standard pre-flop raise had been made.

Assuming a player was at a table that allowed a 4x raise after the flop, what statistical advantage would the player enjoy?

That's the correct line of reasoning. If you're making the 2x Raise at all, then it's because you have the mathematical advantage on that bet, so you would want to raise ANYx that they would allow you to raise in that situation.

In terms of the advantage that a player would have if that player could make the 4x raise after the flop, all you would have to do is go to the Wizard of Odds return table, add the probabilities of every possible way for the player to win with the, "Middle Raise," then multiply that by two to get your expected units gained. After that, you would want to sum the probabilities of the possible ways to lose making the middle raise, then multiply those by two to get the expected number of units lost on those potential outcomes.

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

(0.076036 + 0.004785 + 0.005487 + 0.010405 + 0.000666 + 0.000097 + 0.000004 + 0.038965 + .001620 + 0.001396 + 0.000013) * 2 = 0.278948*

*A few events have a return, but a probability that was so low as to not be expressed on the return table, so are not included.

(0.066196 + 0.000287) * 2 = .132966

In total, this advantage would cause the player to win an additional expected .145982 units, per hand.

Generally speaking, the expected loss of 2.185% relative to the initial two units being bet, so an initial expected loss of 0.0437 units.

If we take our expected gain of .145982 units per hand and subtract the .0437, then we would expect to win .102282 units per initial bet of two units, this would give us a player advantage of 5.1141%.

In theory, this should change nothing about the playing strategy otherwise, all else being equal.

Thanks, Mission.

I'm a recent convert to UTH. I always raise 4x when optimal preflop.

Strangely, many players seem not to grasp that when they are dealt any ace, they have an advantage over the dealer. They think playing cautiously and waiting for a pair is somehow safer. Or they are just mired in the psychology of gambling based on hunches and find optimal play boring.

I don't always know the best play after the flop in borderline cases such as no pair and only a decent high card. Even with my imperfect play, I figure I'm faring better on UTH than on the mindlessly tedious game of placing banker bets on baccarat. I think UTH also tends to comp better than baccarat and blackjack.

Quote: Mission146

Quote: ksdjdj

(snip)
2) Sorry about the wording, the only other times it has happened to me so far, are when the dealer's "next best hand" was a 2 pair or pair (where I had either a better pair or better two-pair, both times),
link to original post

(snip)
I still don't quite get what #2 means, but if it relates back to when the dealer has a flush, I don't think the player winning including all situations in which the dealer has a flush and the player would have otherwise lost is, by itself, advantageous***. That being the case, the situation needing to be more specific than that would not be an advantage, either.

****Also, this assumes that the dealer would never just win some other way, which is not the case. For example:

Dealer: Ah, 8h

Board: Qh, 10h, 5h, Ac, 2d

Player: Qd Kd

Even if the dealer fails to recognize that he has a flush, the player still loses to a dealer pair of Aces v. a player's pair of Queens, so the fact that the dealer had a flush wasn't even needed for the player to still lose this hand. There is no quick way to account for all of these situations that I can think of, but suffice it to say, the dealer doesn't always need the flush that he has to beat the player, so the change in House Edge is not even as good as when we assume the player always wins this.
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IMO this answers #2 (see scenario that happened to me, below).

Scenario:
. Table had at least three players (including myself).
. Dealer pushed forward his cards to make a "pair" (when he had a flush).
. I lost with a hand that was worse than the "dealers' pair".
. But, the player to my right was paid, because he had a "higher pair than the dealer".

Just to point out something. In order to bet 4X it is not enough that you have a (small) advantage over the dealer; because betting 4X deprives you of the opportunity of having more information before making a decision on the next rounds.

To bet 4X preflop: you must have a higher EV with a 4X preflop bet than the EV associated with checking preflop and then making a post-flop '2X or Check' decision based on all the extra information that you have gained.
***************
And in the scenario where a clue-less dealer is allowing you to bet 4X after the flop, there would literally be no reason to bet 4x before the flop. Just wait until postflop, when you will have more information to inform your decision.

Quote: JackSpade

(snip)
One dealer told me I could bet 4x AFTER the flop! I did so twice when having a pair (winning once) before the next dealer came in. On the hand I lost, I knew it was strong enough to bet the standard 2x but hesitated for a moment wondering whether it was also good enough for a 4x raise. I think the answer is that I should never hesitate to raise as large as possible when I have a raise-worthy hand.
(snip)
link to original post

I would guess that if 2x is the correct play, then 4x would also be correct (?)

Otherwise, I would look at any "borderline looking hands" you want, using the calculator here.

Note 1: For working out the raise figure, I would go to "showdown statistics", select "raising", and then add 2 to the "player wins - average prize" and take 2 away from the "dealer wins - average prize"

Note 2: I seem to get the same answer using this calculator and other ones, but I don't know why the "showdown statistics" have a negative "average prize" for the tie, when checking.

Another way for players to gain an advantage in UTH is to reveal their cards to each other. Last time I played, the guy next to me and I were openly talking about our exact hands. Dealer didn't reprimand us in any way.

Once we both had AJ. He checked (but he was a bad player who also checked when he had 99 just because he thought the dealer was running hot). I raised 4x, figuring AJ was still strong enough. If I had a more marginal hand like K6 and knew another player had a king, then I would check. If I had Q6 (normally not a raise unless suited) and knew that nobody else had a queen or a 6, then I might 4x it.

It may also be possible to glean some information about the relative likelihood of high cards being removed from the deck based on how many other players have raised. There are a lot more A, K, Q, J hands that are likely be raised than pairs 33 - TT. So if I see that four players have raised 4x and I have K6, I might check.

Quote: JackSpade

Another way for players to gain an advantage in UTH is to reveal their cards to each other.... (snip)
link to original post

This link probably has the info you want.

Quote: Mission146

That's the correct line of reasoning. If you're making the 2x Raise at all, then it's because you have the mathematical advantage on that bet, so you would want to raise ANYx that they would allow you to raise in that situation.

In terms of the advantage that a player would have if that player could make the 4x raise after the flop, all you would have to do is go to the Wizard of Odds return table, add the probabilities of every possible way for the player to win with the, "Middle Raise," then multiply that by two to get your expected units gained. After that, you would want to sum the probabilities of the possible ways to lose making the middle raise, then multiply those by two to get the expected number of units lost on those potential outcomes.

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

(0.076036 + 0.004785 + 0.005487 + 0.010405 + 0.000666 + 0.000097 + 0.000004 + 0.038965 + .001620 + 0.001396 + 0.000013) * 2 = 0.278948*

*A few events have a return, but a probability that was so low as to not be expressed on the return table, so are not included.

(0.066196 + 0.000287) * 2 = .132966

In total, this advantage would cause the player to win an additional expected .145982 units, per hand.

Generally speaking, the expected loss of 2.185% relative to the initial two units being bet, so an initial expected loss of 0.0437 units.

If we take our expected gain of .145982 units per hand and subtract the .0437, then we would expect to win .102282 units per initial bet of two units, this would give us a player advantage of 5.1141%.

In theory, this should change nothing about the playing strategy otherwise, all else being equal.
link to original post

Bold added by me.

Great analysis but I don’t agree with the bold. I could be thinking about it wrong, but why wouldn’t you check a bunch of the more marginal preflop raise hands until after the flop to see if you hit? I think many of those hands are only raise preflop because of the loss of the potential 4x bet vs only 1x post flop.

Quote: unJon

Great analysis but I don’t agree with the bold. I could be thinking about it wrong, but why wouldn’t you check a bunch of the more marginal preflop raise hands until after the flop to see if you hit? I think many of those hands are only raise preflop because of the loss of the potential 4x bet vs only 1x post flop.
link to original post

You're absolutely right, but please consider it an error in phrasing on my part. What I meant was essentially, "If you would make the Middle Raise for 2x normally, then you would still make it but for 4x; if you would not normally make the Middle Raise for 2x, then you would still not make it."

That said, I'm not going to lie, taking a pass on making the early 4x Raise in favor of waiting hadn't really occurred to me. That being said, the only way I would do that is if I knew the dealer was allowing the post-flop 4x literally EVERY single time a player wanted to do it, otherwise, you risk losing value not to do 4x.

I had something interesting happen to me the other day, and wanted to know if the figures I came up with are correct (or not).

Scenario:
. The players' are normally not allowed to look at their cards, until the dealer has received their cards.
. The current casino policy is "if at least one person at the table looked at their cards early, then you will get a free roll on the side bets + everyone gets paid 1 x the ante ".

Going by the "Wizard Strategy" in the link here the house edge (relative to the ante) is about 1/41.
So, if someone using the "Wizard Strategy" could get this to happen in less than 1/41 of the hands that they played, then they would have a player edge.
Am I correct? (If not, can you post the correct figure).

Thanks in advance

MORE often than 1/41, but otherwise yes, as I understand what you have said.

Was I wrong by a little bit, a factor of about 4.15, or something else?

----
Extra:
For want of a better word, it really was a "perfect storm" type situation when it happened at the table I was playing. (See other things that happened during that round, below):

. I was distracted, buying a drink from a cart (you have to buy them at the place I play at).
. Out of the top / corner of my eye, I thought I saw the dealer move their cards to themselves
. Instead the dealer was moving them all to the discard tray.