Duo Bao

I've never been big on mixing poker with other games, especially when using more than one deck of cards. However, not everyone listens to me. Add to that list the makers of Duo Bao. This is baccarat with a host of side bets that win based on the poker value of the combined Player and Banker hands. If only paigowdan were still around to critique this game.

Please click on the link to see my analysis. As usual, I welcome all questions, comments, and especially corrections.

The question for the poll is would you play Duo Bao?

Depends

Do they give you a free scratch off ticket with each bet placed ?

They could have made the 6-of-a-kind pay 666,666-1 and still have made a huge profit. 60,000 is a joke.

Hi, Mike. First, I want to make sure that I understand this game, and your analysis, properly.

Based on the total number of permutations, it is clear that you are including every permutation of 6 cards drawn from an 8 deck shoe. However, many of these permutations are not viable baccarat hands and cannot actually occur. For instance, I think that 20,160 permutations result in 4h 4h 4h 4h 4h 4h. In reality, this hand would be discontinued after the first four cards due to the natural 8's. So these permutations would pay off the 3 of a kind and 4 of a kind bets, but would not pay off the 5 of a kind, 6 of a kind and flush bets. Do I understand this correctly?

I would not play this game due to the horrible odds. But it seems to me that even the most optimistic jackpot chaser would lose interest in this game fairly quickly due to the infrequency of the payouts. Is anybody going to feed a dollar to the six-of-a-kind bet on every hand, knowing that it is unlikely that they will ever get even a penny back during their lifetime? I would think a better approach would be the PGP fortune bet model, which combines all the possible results into a single bet. This way the bettor would see a small positive result every few hands and they might convince themselves that they're winning, even though the long term result is grossly in the house's favor.

Quote: PapaChubby

Hi, Mike. First, I want to make sure that I understand this game, and your analysis, properly.

Based on the total number of permutations, it is clear that you are including every permutation of 6 cards drawn from an 8 deck shoe. However, many of these permutations are not viable baccarat hands and cannot actually occur. For instance, I think that 20,160 permutations result in 4h 4h 4h 4h 4h 4h. In reality, this hand would be discontinued after the first four cards due to the natural 8's. So these permutations would pay off the 3 of a kind and 4 of a kind bets, but would not pay off the 5 of a kind, 6 of a kind and flush bets. Do I understand this correctly?

I must look more stupid than I thought. Of course I only counted viable baccarat hands. I shouldn't have to even say that. The total permutations equals 416!/408! because I correctly weighted 4- and 5-card hands.

My apologies. I meant no disrespect, and certainly didn't mean to imply that you might have done anything inappropriate.

First, I was making sure I understood the rules of the game: a) does the deal stop when the baccarat hand is resolved, or b) does the dealer always continue to 6 cards to resolve the side bet. My understanding is (a).

Second, assuming (a), I was envisioning the structure of the program which would be used to analyze the game. My first thought was to loop thru every permutation of initial 4 cards. If additional cards are required, consider these a subset of the initial 4. Based on your presentation, it appears that you are looping through every 6 card permutation. Upon further consideration, a hybrid approach is probably most efficient: Set up a 6 card looping structure. After the first 4 or 5 cards are selected, determine whether execution of the inner loops is warranted to determine additional cards. If not, calculate the payouts based on the 4 or 5 cards and apply the results to all of the 411 or 169,322 permutations contained therein. And I'm guessing that this is probably what you did.

Quote: sodawater

They could have made the 6-of-a-kind pay 666,666-1

why not? they would then point to the sign that says payouts are limited to X amount !

or just put up the sign later.

If it's good enough for Sabrina Yu, it's good enough for me!


Who is Sabrina Yu?

Quote: PapaChubby

First, I was making sure I understood the rules of the game: a) does the deal stop when the baccarat hand is resolved, or b) does the dealer always continue to 6 cards to resolve the side bet. My understanding is (a).

(a) Is correct. There are two ways you could analyze this:

1. Loop through all 416!/408! permutations of cards but ignore cards that would never get played because drawing rules forbid it.
2. Only loop through the possible combinations and appropriately weight situations with 4 or 5 total cards. This is how I did it.

Quote: Wizard

I've never been big on mixing poker with other games, especially when using more than one deck of cards. However, not everyone listens to me. Add to that list the makers of Duo Bao. This is baccarat with a host of side bets that win based on the poker value of the combined Player and Banker hands. If only paigowdan were still around to critique this game.

Please click on the link to see my analysis. As usual, I welcome all questions, comments, and especially corrections.

The question for the poll is would you play Duo Bao?

I recall seeing $200,000 Carribean-Stud JP's (odds about 1 in 650,000) and thinking "Its STILL not a good bet". Wait until $235,000+. 60 Long on 850,000 to 1... PASS.

Could we EVER see a 4-card analog to Paigow Tiles ??? Not holding my hand on my butt for that one. And paigowdan has left the building, walking with Elvis.

98

Duo Bao Analysis

Bet Permutations
Six of a kind 5,872,124,160
Five of a kind 356,942,987,520
Four of a kind 12,630,904,546,560
Three of a kind 261,745,356,391,680



My program:
Six of a kind 5,872,124,160
Five of a kind 356,942,987,520
Four of a kind 12,630,904,546,560
Three of a kind 261,128,938,702,080

Banker 2,292,252,566,437,880
Player 2,230,518,282,592,250
Tie 475,627,426,473,216
All 4,998,398,275,503,360

Hi,
Compare the results from my program and the numbers from Duo Bao Analysis, all the numbers looked good, except "Three of a kind". I don't know how to find the error in my program.
Any suggestions?

I just found that,
261,745,356,391,680 - 261,128,938,702,080 = 616,417,689,600
and this 616,417,689,600 is the number of "two sets of 'three of a kind' in one round"
like player "2,1,2", banker "1,2,1"

Quote: 7up

261,745,356,391,680 - 261,128,938,702,080 = 616,417,689,600
and this 616,417,689,600 is the number of "two sets of 'three of a kind' in one round"
like player "2,1,2", banker "1,2,1"

Mike, is there any chance that you double count the above 616,417,689,600 ?

Quote: 7up

Mike, is there any chance that you double count the above 616,417,689,600 ?

Sorry for the tardy reply. It looks like you are absolutely right. I am running running my program now to verify, but it looks like I did double count those situations. The program will finish in about 90 minutes. Thank you for bringing this to my attention.

多宝
Duo bao
Many/multi treasure

Quote: BleedingChipsSlowly

多宝
Duo bao
Many/multi treasure

I just got a second opinion and it seems you're right. Thank you for the correction.

Quote: 7up

Mike, is there any chance that you double count the above 616,417,689,600 ?

I adjusted for the double-counting problem. My new total for a three of a kind is 261,128,938,702,080.

what will be the Bet Permutations for 2 pairs in this game? is there any manual calculation using excel spreadsheet?