Joker in Pai Gow Poker: a card - or just a connector?

The casino cheated, plain and simple. Typical in Indian joints. You people will never learn. DON'T PLAY IN AN INDIAN CASINO!!!!!

Quote: Ibeatyouraces

The casino cheated, plain and simple. Typical in Indian joints. You people will never learn. DON'T PLAY IN AN INDIAN CASINO!!!!!

Wizard never said this happened in an Indian casino. WA is home to many cardrooms.

Quote: Ibeatyouraces

The casino cheated, plain and simple. Typical in Indian joints. You people will never learn. DON'T PLAY IN AN INDIAN CASINO!!!!!

Lol. Biased much?


ZCore13

Nothing to do with being biased. I'm just giving fair warning to the suckers out there. I'd never play in your joint either. And it has nothing to do with AP.

I have had to make that ruling in several casinos in different jurisdictions, Indian and Commercial. The joker should be the next highest card in the flush, and the player with AKQJ2 should beat the dealer with AK*86.

By the way, since nobody in the thread has it correct, Pai in Chinese means Card, Pai Gow- Card 9.

Quote: Ibeatyouraces

The casino cheated, plain and simple. Typical in Indian joints. You people will never learn. DON'T PLAY IN AN INDIAN CASINO!!!!!

We can't blame the Indians for this one. This happened in one of the little card-game-only casinos in Washington. There are lots of them. I asked my source for the name but he wouldn't tell me, knowing I would embarrass them over this.

Let's keep in mind we're talking about the same game that treats the A2345 straight as the second highest. I think that is equally stupid and un-poker like.

Miplet, if you would be so kind, please ask about this hypothetical situation the next time you're in a WA casino.

Quote: Wizard

Miplet, if you would be so kind, please ask about this hypothetical situation the next time you're in a WA casino.

Yep. I’ll ask at any I go to.

Quote: miplet

Yep. I’ll ask at any I go to.

Thank you.

As long as the rule interpreting the joker's rank in a flush is enforced identically for the player and dealer, it should have no impact on HE or optimal strategy. But how much of a difference does this rule ambiguity make on a specific hand? According to my calculations, never more than ΔEV= 0.0034. Details appear below.
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I've selected a couple of player hands that are (I think) maximally impacted by the ambiguity in the rule about the effective rank of the joker when both the joker and an ace are used to make a flush.

1. If the player hand has a natural AKQ -high flush and no joker such as

Bottom: A♠ K♠ Q♠ J♠ 8♠ Top: 7♣ 6♣

then what is the chance that the dealer will show up with a Joker-Ace flush in the bottom to beat the player's bottom?

Well, I can't calculate that rigorously with my composition-dependent PGP calculator, because I don't report whether the joker was used in the 5-card hand in the bottom or in the two-card hand on top. But I have figured out a way to calculate an approximate answer that should be pretty good; the probability that the dealer will have a Joker-Ace flush in the bottom is roughly 0.0033 or 0.33%. So the ambiguity in EV of this hand arising from the ambiguity in the rules is ΔEV= 0.0033.

2. Now, let's consider a player hand that has a Joker-Ace flush in the bottom. Specifically, I have selected the hand that I think is maximally affected by the ambiguity in the rule about how to interpret the joker in an Ace-joker flush:

Bottom: Joker-A♠ 6♠ 3♠ 2♠ Top: 2♦ 2♣

Using the more conventional ruling this hand has an AK632 flush on the bottom and will lose to better AK-high flushes -which in this case is any AK-high flush except an AK632 flush in hearts - with which it will tie. However, with the interpretation that the Joker plays as a second A♠, this flush will win against any AK-high flush (and indeed against any flush).

Using my composition-dependent PGP calculator, I calculate that this makes a difference of 0.0034 in the EV of this player hand. Again, the value of ΔEV= 0.0034 is an upper bound on the effect of this rule ambiguity on any given player hand with a bottom flush with the joker and an ace.
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Quote: gordonm888

As long as the rule interpreting the joker's rank in a flush is enforced identically for the player and dealer, it should have no impact on HE or optimal strategy. But how much of a difference does this rule ambiguity make on a specific hand? According to my calculations, never more than ΔEV= 0.0034. Details appear below.
******************************
I've selected a couple of player hands that are (I think) maximally impacted by the ambiguity in the rule about the effective rank of the joker when both the joker and an ace are used to make a flush.

1. If the player hand has a natural AKQ -high flush and no joker such as

Bottom: A♠ K♠ Q♠ J♠ 8♠ Top: 7♣ 6♣

then what is the chance that the dealer will show up with a Joker-Ace flush in the bottom to beat the player's bottom?

Well, I can't calculate that rigorously with my composition-dependent PGP calculator, because I don't report whether the joker was used in the 5-card hand in the bottom or in the two-card hand on top. But I have figured out a way to calculate an approximate answer that should be pretty good; the probability that the dealer will have a Joker-Ace flush in the bottom is roughly 0.0033 or 0.33%. So the ambiguity in EV of this hand arising from the ambiguity in the rules is ΔEV= 0.0033.

2. Now, let's consider a player hand that has a Joker-Ace flush in the bottom. Specifically, I have selected the hand that I think is maximally affected by the ambiguity in the rule about how to interpret the joker in an Ace-joker flush:

Bottom: Joker-A♠ 6♠ 3♠ 2♠ Top: 2♦ 2♣

Using the more conventional ruling this hand has an AK632 flush on the bottom and will lose to better AK-high flushes -which in this case is any AK-high flush except an AK632 flush in hearts - with which it will tie. However, with the interpretation that the Joker plays as a second A♠, this flush will win against any AK-high flush (and indeed against any flush).

Using my composition-dependent PGP calculator, I calculate that this makes a difference of 0.0034 in the EV of this player hand. Again, the value of ΔEV= 0.0034 is an upper bound on the effect of this rule ambiguity on any given player hand with a bottom flush with the joker and an ace.
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Fwiw, and I have not done the math, I think the EV on the last hand listed would always be maximized by putting A-joker in the top hand and trip deuces in the bottom, so I don't think it would be correct to hold this no matter how the Joker completes the flush. I could be wrong.

Quote: beachbumbabs

Fwiw, and I have not done the math, I think the EV on the last hand listed would always be maximized by putting A-joker in the top hand and trip deuces in the bottom, so I don't think it would be correct to hold this no matter how the Joker completes the flush. I could be wrong.

You are correct. I should not have chosen the pair of twos for the top hand. When I change one of those 2s to a 3 -so the top hand is 32, I get the same result when quoted to 4 digits.

I agree the rule of the joker counting as any card in a flush cuts equally both ways. My point is that if a casino is going to claim something ridiculous in the rules, they should at least produce the rule clearly in writing.

My casino rules the joker is the highest available card in the flush, not a second ace. When it was brought up for discussion, I called a cardroom in western WA, and spoke to their pit boss about it. As luck would have it, he himself had just spoken to the WSGC about it. He said the ruling was that the joker cannot be a second ace in a flush.

This was about five years ago. Wizard, I'd love to hear any updates if you get any, and I'm sure others would too.

I just sent an email to the gaming commission. We will see if they respond.

I asked Bill Zender for some more details. He says in the 1980's the Desert Inn was still treating the joker in a flush as an ace, even if there already was an ace in it. When he started working there he convinced them it was a stupid rule and they changed it to how it usually is now.

He added that some casinos have treated it as a "blank" card, which I think PGD asked about in the original post. In other words, a value less than 2. For example,

Suited A975-joker would lose to suited A9752, because the joker either has no rank or is ranked lower than 2, however you wish to look at it.

Quote: Wizard

He added that some casinos have treated it as a "blank" card, which I think PGD asked about in the original post. In other words, a value less than 2. For example,

Suited A975-joker would lose to suited A9752, because the joker either has no rank or is ranked lower than 2, however you wish to look at it.

In that case, 4567-joker suited would not be a straight flush.

What an interesting pickle... I think there's a combination of facts that point to the conclusion the joker should have been played as the Qh.

1) Standard poker rankings. Yes, in "anything's wild" game there is such a thing as 5 of a kind. Still, there is standard poker rankings, which do not include duplicating a card, such that you can not have a "double ace high" flush.

2) The joker takes the value of a card, whenever it's played. Ace when not being used in a straight or flush. When in a straight, it's a very specific rank. I don't see why that wouldn't be the same case for a flush, especially considering a straight flush as IBYA pointed out above. 4h-5h-6h-7h-Joker. The joker becomes either the 3h or 8h, which again specifically has a rank.

3) As row pointed out, the dealers "slot" the cards from highest to lowest rank. I'd be willing to bet when this dealer set the hand, it went: "Ah, Kh, Joker, x, x" putting the Kh before the joker. While I've never had to deal with this situation before, I have seen every dealer with a joker place it in a ranking position of "next available."

I wonder if we'd all be arguing for the player had this hand been the other way around and the player had won? =) I know I would argue the same, because the idea of your final 5 card poker hand being Ah-Ah is just stupid for the game of poker.

I have specifically asked pit bosses about this, and they have always answered that the joker is the highest available card not already naturally in the hand, thus, not two aces in a flush ever. I 'think' I asked at the Rio and my local Indian casino. The phrase they have used is, 'it is an ace, unless it fills a straight or flush.' They don't say, 'it is an ace unless it fills a straight'.

Quote: Ibeatyouraces

In that case, 4567-joker suited would not be a straight flush.

I should have been more clear. It can substitute for a specific card to complete a straight or straight flush. If used to complete a flush, it has no rank.

I got a response. They want to know what casino. Below is their email with mine below that. What should my reply be?
__________________
Bobby:

Below, I copied and pasted the email you sent to the Washington State Gambling Commission. What casino did this incident happen in?

Thanks,
name redacted
Washington State Gambling Commission
number redacted



Hi

We are currently discussing a recently a disputed pai gow poker hand in Washington. Here is a quote from the thread that explains it.
“
Dealer: Ah, Kh, 8h, 6h, joker ( where h=hearts)
Player: As, Ks, Qs, Js, 2s (where s=spades)

The player argued he won the comparison, because the dealer's joker would substitute for the highest available heart not already used in the dealer's high hand, which would be the queen. So, the player's AKQJ2 would beat the dealer's AKQ86.

However, the casino argued that the joker substituted for another ace of hearts, giving the win to the dealer. I was told every dealer in the casino agreed with that ruling. In other words, the dealer had an AAK86 flush, which beats a AKQJ2 flush.

What is supposed to happen in this situation?”

https://wizardofvegas.com/forum/gambling/tables/7784-joker-in-pai-gow-poker-a-card-or-just-a-connector/4/#post609901

We would like an official gaming commission response if possible.

Thanks
Adam "Bobby" Cohen aka miplet
PS
If you want to reply in the thread that would be awesome, otherwise I’d like permission to quote your response.

I went to Angel of the Winds Casino last night. I only asked one dealer. She said the Joker would be a second Ace. I probably should have asked more than one dealer.

Quote: miplet

I went to Angel of the Winds Casino last night. I only asked one dealer. She said the Joker would be a second Ace. I probably should have asked more than one dealer.

You probably should have asked a pit boss and gotten her/his name. If the pit boss affirmed what the dealer told you, you could then report something specific to the WA game commission, even if you could not name the original casino.

Just my 2 cents. But, many thanx for your efforts to follow up on this crazy Pai Gow poker ruling. Half a loaf is better than nothing.

I asked at The Crazy Moose in Mountlake Terrace: it’s the highest card not already in the flush. I’m not the kind of person to ask the Floor for an answer unless it affects my hand, so I didn’t ask anyone else.

Quote: miplet

I asked at The Crazy Moose in Mountlake Terrace: it’s the highest card not already in the flush. I’m not the kind of person to ask the Floor for an answer unless it affects my hand, so I didn’t ask anyone else.

I understand. So, how do you plan to respond -- if at all -- to Washington Gaming? Seems you checked "some casinos," and got the answer both ways: highest available card and second ace in the same suit.

As for myself, I wouldn't bother the suit if the pit was busy. But, if it's early and players are few, I ask. The suits want me to play, and if I don't understand, I might decide not to play.

Quote: miplet

I went to Angel of the Winds Casino last night. I only asked one dealer. She said the Joker would be a second Ace. I probably should have asked more than one dealer.

Thanks Miplet for your legwork on this. I feel somewhat vindicated on this in my claim that some casinos in Washington do count a joker in a flush as an ace, whether or not there already is one naturally.

If you return, can you please try to get a confirmation of that? I would like to mention the casino by name in my next Ask the Wizard question.

Quote: Wizard

Thanks Miplet for your legwork on this. I feel somewhat vindicated on this in my claim that some casinos in Washington do count a joker in a flush as an ace, whether or not there already is one naturally.

If you return, can you please try to get a confirmation of that? I would like to mention the casino by name in my next Ask the Wizard question.

Just asked another dealer from Angel of the Winds (I haven’t been back yet, but he comes to my work sometimes) and he said that the other dealer must have misunderstood my question as you can’t have 2 Aces in a flush. It would be whatever the highest card not already in the flush.

Next stop: Quil Ceda Creek Casino, a tribal casino. It’s the highest card not in the flush. The Floor person agreed and even tried to find something I could look at in a pamphlet, but couldn’t find one.

There isn’t any other place I go to regularly, but I might venture out and ask at some other nearby card rooms.