Potential positive edge in Ultimate Texas Hold 'em

Hello, so let me start off by saying I am a casino dealer in Perth, Australia. Relatively recently we've brought in UTH. I've noticed that one of our rules is different to yours (from wizardofodds), namely that when the dealer wins, but does not qualify, BOTH the anti and blind push (as opposed to anti-push, blind-lose). I assume this would definetly change the strategy (must small-raise any non-paired board except when 4 to a flush or open-ended straight on board) but I'm wondering how much the edge is affected, and whether it is enough for a positive edge, as I suspect it is infact an error in interpreting the game. Thanks for your time.

Quote: Sassafras

Hello, so let me start off by saying I am a casino dealer in Perth, Australia. Relatively recently we've brought in UTH. I've noticed that one of our rules is different to yours (from wizardofodds), namely that when the dealer wins, but does not qualify, BOTH the anti and blind push (as opposed to anti-push, blind-lose). I assume this would definetly change the strategy (must small-raise any non-paired board except when 4 to a flush or open-ended straight on board) but I'm wondering how much the edge is affected, and whether it is enough for a positive edge, as I suspect it is infact an error in interpreting the game. Thanks for your time.

The table labeled "Return Table" on Wizard's UTH page shows that the above scenario (dealer does not qualify but wins) is small but not insignificant. Its probability is 0.5676%, which is 0.1698% (for small raise) + 0.0287% (for medium raise) + 0.3691% (for large raise.)

If the player does not change his strategy based on the blind's pushing, then the house edge would decrease by 0.005676. So, the house edge of your game would be 0.021850 - 0.005676 = 1.617%.

The Wizard would have to answer your question about what strategy changes the player would have to make to decrease the house edge further.

Quote: ChesterDog

The table labeled "Return Table" on Wizard's UTH page shows that the above scenario (dealer does not qualify but wins) is small but not insignificant. Its probability is 0.5676%, which is 0.1698% (for small raise) + 0.0287% (for medium raise) + 0.3691% (for large raise.)

If the player does not change his strategy based on the blind's pushing, then the house edge would decrease by 0.005676. So, the house edge of your game would be 0.021850 - 0.005676 = 1.617%.

The Wizard would have to answer your question about what strategy changes the player would have to make to decrease the house edge further.

Edit: well, crap, I was wrong, but I'll leave this up here anyway. I thought the OP said they pushed the ante and PLAY bets, not the ante and BLIND bets. Chester has the HE correct, best I can tell. However, I still think the HE is misleading, and needs an EOR calculation to evaluate the impact. Using ChesterDog ' s figure of 1.617%, the EOR would be .389%, still incredibly low compared to any other HE or equivalent.

Original post follows.

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I could be wrong, but I think your analysis is incomplete and consequently underestimates the impact of this rule change.

You can't simply use rate of occurrence because the bet amounts are different. You have to multiply the rate of occurrence by the unit not collected amount (I think) to evaluate the loss to the house. So

.1698% x 1 unit
+ .0287% x2 units
+ .3691% x4 units
= 1.7036%

House edge 2.1850% becomes .4814%

This is further eroded by the Wizard's Element of Risk rule, which attempts parity among games with bets beyond a single pre-decision amount (most poker and carnival games except Paigow tiles/poker) and simple bet structure games (most classic casino games like craps, roulette, baccarat, and most blackjack hands).

He does this by calculating the average total bet with optimal strategy, not just the ante, and dividing the HE by that (because, again, the additional bets magnify the amount at risk, and HE only calculates the ante amount, not the blind or play).

For UTH, the average hand is worth 4.152 ante units. So the element of risk is a mere .1159% Not quite a player advantage, but I'd love to play that game and take my chances, let's just say that!

Bracing for impact. I'm sure I'll get beaten about the head and shoulders by the APs for analyzing this, assuming I've done it correctly.

I will say I've been playing optimal strategy for 4 years now and working hard to perfect the details. This means many hours of live play and hundreds if not more of other players observed. I have not met ONE. That's ZERO. Other players who play optimal strategy (it's very hard), let alone understand how to calculate their kickers. So I think your casino is safe to do this if they want to and still make plenty of money on it. Time will tell.

Quote: beachbumbabs

...You have to multiply the rate of occurrence by the unit not collected amount (I think) to evaluate the loss to the house. So

.1698% x 1 unit
+ .0287% x2 units
+ .3691% x4 units...

In effect, I did .1698% x 1 unit + .0287% x 1 unit + .3691% x 1 unit = .005676 unit. I wouldn't multiply by the size of the raise, because only the constant blind part of the bet is affected by the OP's casino's rule variation. (The raise is still lost in his casino when the dealer wins but does not qualify.)

Quote: ChesterDog

In effect, I did .1698% x 1 unit + .0287% x 1 unit + .3691% x 1 unit = .005676 unit. I wouldn't multiply by the size of the raise, because only the constant blind part of the bet is affected by the OP's casino's rule variation. (The raise is still lost in his casino when the dealer wins but does not qualify.)

Yes, thanks, I found my error and edited the start of my post while you were writing this. I misread the OP and thought they were pushing the play bet, not the blind, in addition to the ante. I agree with your calculation, but I think the EOR formula must be used to evaluate the true parity.

Thank you both for your input, I'd still be interested in knowing any differences in strategy, if anyone is capable/bored, as when people ask me for advice I like to be able to be correct.

Quote: Sassafras

Thank you both for your input, I'd still be interested in knowing any differences in strategy, if anyone is capable/bored, as when people ask me for advice I like to be able to be correct.

I think someone playing a kicker could look around at how many other people 2-bet and reduce the dealer's outs by 1 per those hands. Except for sequential or suited flops, you could nearly guarantee those are people who paired up or misplayed an ace. Table chatter about hitting on the flop for 4-bets and river for other 1 bets could also help. The practical effect would be probably one rank better for your kicker on a full table most hands.

Combined with the "pot value" of potentially saving 2 bets for 1, rather than 1 for 1, it might even be worth 2 ranks.

And I agree about small betting unpaired boards with nearly anything. Might even make Kx or Qx worth a 2-bet post-flop.

However, the part I suggested at the top isn't so much strategy as indirect collusion, so probably doesn't help your advice- giving as a dealer. Think that will have to come from the Wizard if he has the time. Hopefully he can just change those 3 values in his spreadsheet and run his strategy analysis again.

Quote: ChesterDog

The table labeled "Return Table" on Wizard's UTH page shows that the above scenario (dealer does not qualify but wins) is small but not insignificant. Its probability is 0.5676%, which is 0.1698% (for small raise) + 0.0287% (for medium raise) + 0.3691% (for large raise.)

If the player does not change his strategy based on the blind's pushing, then the house edge would decrease by 0.005676. So, the house edge of your game would be 0.021850 - 0.005676 = 1.617%.

Sorry for the late arrival. I agree with the above. To be specific, here are the number of combinations where the player would save a unit, according to the size of the raise:

Small 47,223,220,344
Medium 7,978,353,108
Large 102,655,952,400
Total 157,857,525,852

There are 27,813,810,024,000 total combinations, so the savings is 157,857,525,852/27,813,810,024,000 = 0.005675509, assuming no change in strategy.

It would be easy to say that the player should take more chances with the raises under this rule. I leave the specifics up to the reader.

Thanks Wizard for your time. I'm not well versed in this level of probability calculation, but given my own approximation of strategy is close to correct, wouldn't the number of occurences where the player saves a unit for the small raise be drastically higher? But I guess that would be countered by times where they didn't fold where they previously would have and lose an extra unit.

I'd also like to say a big thank you for everything you've done with your sites, they are a very valuable resource

Quote: Wizard

It would be easy to say that the player should take more chances with the raises under this rule. I leave the specifics up to the reader.

If the player is to just "wing it" then I'd say raise 4x with any King, 4x with a Queen except not if with 2-4 unsuited [in other words same as normal rule with a K], 4x with 8-Jack suited. Or better of course.

2x raise changes I'd have to think about a little more.

1x raising - if contemplating the kicker situation, go with any Jack immediately, quick with 10 or 9 if possibly in play.