Pai gow and prepaid commission

I am relly concerned about this issue with the prepaid commission.
I cannot see the upside to this for the player at all and it is keeping me up tonight!

If I walk up a table with $100,
I bet $20, I now have $80 on hand.
I win.
I can either receive $19 plus the original $20 wager or
I pay the dealer $1 and I receive $20 plus the original $20 wager.
I have $119.

If I walk up with $100
I bet $21, I now have $79 on hand.
I win.
The dealer keeps $1 and I am paid $20 plus the original $20 wager.
I have $119.

How is paying $21 for $40 any different than paying $20 for $39?

There is no gain by playing this increased wager.
However, if I lose...
I have $80 on hand without prepaying and only $79 after placing the prepaid commission wager!

It seems to me that increasing the bet size by 5% only means that at the end of my session I will be down an additional 5% of any potential losses. I am not surprised the casinos allow this play! It moves the game faster with no upside for the player.

Quote: WongBo

If I walk up with $100
I bet $21, I now have $79 on hand.
I win.
The dealer keeps $1 and I am paid $20 plus the original $20 wager.
I have $119.

How is paying $21 for $40 any different than paying $20 for $39?

Actually, you would have $120 with this pre-paid commission bet, not $119. If it helps you understand why pre-paying is better, you can think of the part of your bet that is doing the "pre-paying" as a commission-free part of your total bet.

For example, a normal wager of $105 would stand to win $99.75, whereas a pre-paid commission wager of $105 would stand to win $100. Obviously, if you lose, the net is -$105 in both cases.

Just realized I forgot to count the extra dollar in the original $21 wager and that I would be wagering $21 to get a return of $41!
It makes sense to me now I can go back to studying the optimal strategy charts. Sorry for the brain freeze.

There is a slight difference that benefits the player.

Case A.) You bet $20 and win $19. Your payout is 19/20 = 0.950 (exact).
Case B.) You bet $21 and win $20. Your payout is 20/21 = 0.95238+.

Considering no banking and the same house rules, the house advantage is reduced from 2.73% in Case A.) to 2.662% in Case B.).

I have not seen the prepaid commission on any bet less than $100. I once was playing, and cannot remember where, a player playing $105 each hand. I asked if I could do the same at $21 and was told no. They said the extra $1 would pay a full quarter commission, so of course I didnt do it. Of course they allow you to toke a dollar bet commission free.

Horseshoe Hammond allows $1 prepaid commission on $20.

Quote: 98Clubs

There is a slight difference that benefits the player.

Case A.) You bet $20 and win $19. Your payout is 19/20 = 0.950 (exact).
Case B.) You bet $21 and win $20. Your payout is 20/21 = 0.95238+.

Considering no banking and the same house rules, the house advantage is reduced from 2.73% in Case A.) to 2.662% in Case B.).

Here is how wizardofodds.com webmaster and pai gow expert JB explained it to me:


Hello,

The reason for the apparent discrepancy is that you are examining individual scenarios and not the bigger picture.

If you play optimally against the traditional house way (whether prepaying the commission or not), the outcomes are:

Win   = 216,608,452
Push  = 301,677,508
Lose  = 217,995,040
Total = 736,281,000

If you do not prepay the commission (let's say that you bet $20 per hand to win $19), here are the results:

Win   = Net payoff of ( 19/20) x (216608452/736281000) = +0.279483
Push  = Net payoff of (  0/20) x (301677508/736281000) =  0.000000
Lose  = Net payoff of (-20/20) x (217995040/736281000) = -0.296076
------------------------------------------------------------------
Total =                                                  -0.016593

If you do prepay the commission (let's say that you bet $21 per hand to win $20), here are the results:

Win   = Net payoff of ( 20/21) x (216608452/736281000) = +0.280183
Push  = Net payoff of (  0/21) x (301677508/736281000) =  0.000000
Lose  = Net payoff of (-21/21) x (217995040/736281000) = -0.296076
------------------------------------------------------------------
Total =                                                  -0.015892

So by not prepaying the commission, the house advantage is 1.6593% whereas by prepaying it, the house advantage is reduced to 1.5892%.

Thus, it is better to prepay the commission overall.

- JB

Webmaster, WizardOfOdds.com

I have another question for any pai gow playing mathematician...

I understand that there are 35960 possible four-tile combinations... Combin(32,4)

I have read there are 3620 unique four-tile combinations
Consisting of 1820 no-pair combinations, 1680 one-pair combinations, and 120 two-pair combinations.
I can see that combin(16,4) yields the 1820 no-pair combinations
And that 16*combin(15,2) yields 1680 one-pair combinations
And that combin(16,2) yields 120 two-pair combinations.

I am assuming the difference between the 35960 combinations and the 3620 unique combinations
Is caused by the fact that there are only 21 unique tiles and 11 duplicates.

Could someone knowledgeable delve into the details of theses equations and provide more insight?


By the way, here is an excellent resource of sortable tables of all 960 possible hand values:
http://pokerstrategy.us/poker_articles/gambling_faq.htm

I'm thinking really hard, but I can't figure out your comment about 21 unique tiles. I think maybe you're counting each tile of the mixed pairs as unique tiles. But they play the same in a hand, so they're really not.

There are 16 pairs of tiles in the deck. So I'd say there are 16 unique tiles and 16 duplicates.

For each of the no-pair combinations, there are 16 ways to replace some or all of the tiles with their duplicate, arriving at effectively the same hand.

A B C D
A' B C D - A B' C D - A B C' D - A B C D'
A' B' C D - A' B C' D - A' B C D' - A B' C' D - A B' C D' - A B C' D'
A' B' C' D - A' B' C D' - A' B C' D' - A B' C' D'
A' B' C' D'

For each of the one-pair combinations, you're stuck with the pair. But there are 4 ways to select the other two tiles from among the originals and duplicates.

A A' B C - A A' B' C - A A' B C' - A A' B' C'

There is no way to introduce alternates into the two-pair combinations.

A A' B B'

So the total number of possible hands is 1820 x 16 + 1680 x 4 + 120 = 35960.

Back to the prepaid commission issue, I have a question for the Vegas-ites.

Do places like MGM Grand that don't use quarters on the tables allow you to prepay commission? Also, do they allow you to prepay commission on banking hands? I'd think the latter would be no, but I'm not sure about the first question.

My best educated statement referenced from the North East USA... If you don't see quarters you won't be able to pre-pay commission under $20. $21 for $20 "should" be allowed.

When I play at Mohegan Sun in CT, they allow prepaid commission ($25 minimums).
I am curious about the trend in the AC casinos.
Does anyone know if $25 is a fairly standard minimum in AC, and whether or not prepaying commission is accepted there?
While I am asking, does anyone know of any tables in AC with a minimum below $25?

Quote: WongBo

When I play at Mohegan Sun in CT, they allow prepaid commission ($25 minimums).
I am curious about the trend in the AC casinos.
Does anyone know if $25 is a fairly standard minimum in AC, and whether or not prepaying commission is accepted there?
While I am asking, does anyone know of any tables in AC with a minimum below $25?

Last time I was in AC, in December, Showboat had one table of Pai Gow for $15 in the Asian room. It was upped to $25 for the evening. I saw a Pai Gow table, empty on a Monday morning, at ACH for $10. Otherwise, $25 seems to be the standard in AC. Prepaying commission, I believe, is not allowed, but they do allow banking and have multiple deliveries posted. Caesars does have $20 chips, but the tables were all $25 at the time I played there.

Nevermind- found the discussion. :)

Borgata also has the $20 yellow chips in the asian area. Everytime I've played there, minimums have been $20 for all the tables. I've asked, none of Borgata, Harrah's, Showboat, Taj, Resorts or Bally's allow prepaid commission. Both Mohegan and Foxwoods allow prepaid commisson for any amount.

Quote: jake0508

Borgata also has the $20 yellow chips in the asian area. Everytime I've played there, minimums have been $20 for all the tables. I've asked, none of Borgata, Harrah's, Showboat, Taj, Resorts or Bally's allow prepaid commission. Both Mohegan and Foxwoods allow prepaid commisson for any amount.

Foxwoods does not have prepaid commission, only Mohegan does.

Haven't played there in almost a year, but last time I did, Foxwoods allowed prepaid commission. Maybe they changed the rule?

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