Dragon Poker
Poll
 | 3 votes (15.78%) | ||
| | 4 votes (21.05%) | ||
| | 10 votes (52.63%) | ||
| | 3 votes (15.78%) | ||
| No votes (0%) | |||
| | 2 votes (10.52%) | ||
| | 1 vote (5.26%) | ||
| | 4 votes (21.05%) | ||
| | 2 votes (10.52%) | ||
| | 3 votes (15.78%) |
19 members have voted
September 29th, 2018 at 1:13:23 PM
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I hear the Rio is hosting a field trial of the game Dragon Poker. Click that link to play their demo, which is nicely done, especially the "help" button. Basically, it seems like a cross between Three Card Poker and Ultimate Texas Hold 'Em, but played with a modified deck, as follows, in rank order, from highest to lowest:
3 Fire Dragons
3 Water Dragons
1 wild Gold Dragon
7 Phoenixes (what is the plural of phoenix?)
8 Tigers
9 Pandas
10 Monkeys
12 Rabbits
I will try to check it out shortly, maybe even this evening.
The help pages suggest raising with a Phoenix-Panda or higher.
The question for the poll is would you play Dragon Poker?
3 Fire Dragons
3 Water Dragons
1 wild Gold Dragon
7 Phoenixes (what is the plural of phoenix?)
8 Tigers
9 Pandas
10 Monkeys
12 Rabbits
I will try to check it out shortly, maybe even this evening.
The help pages suggest raising with a Phoenix-Panda or higher.
The question for the poll is would you play Dragon Poker?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 29th, 2018 at 1:19:31 PM
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I'll wait till you tell me what the house edge is before I decide to play it.
But I am at least interested enough to wait for the analysis.
But I am at least interested enough to wait for the analysis.
September 29th, 2018 at 1:26:51 PM
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Quote: TigerWuI'll wait till you tell me what the house edge is before I decide to play it.
But I am at least interested enough to wait for the analysis.
I very wise position. For now, I can at least do the side bets. Stay tuned.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 29th, 2018 at 2:01:35 PM
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Here is my analysis of the 3 Card Bonus. Any agreements or disagreements from the other math wizards on the forum?
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Three Dragons | 40 | 35 | 0.001494 | 0.059763 |
| Three Phoenices | 30 | 56 | 0.002391 | 0.071715 |
| Three Tigers | 15 | 84 | 0.003586 | 0.053786 |
| Other trips | 10 | 571 | 0.024375 | 0.243746 |
| Two Dragons | 4 | 966 | 0.041236 | 0.164945 |
| Two Phoenix | 2 | 1,218 | 0.051994 | 0.103987 |
| Two Tigers | 1 | 1,480 | 0.063178 | 0.063178 |
| Other | -1 | 19,016 | 0.811748 | -0.811748 |
| Total | 23,426 | 1.000000 | -0.050628 |
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 29th, 2018 at 2:10:43 PM
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Here is my analysis of the Dragon Bonus. I assume the top two awards must be natural (otherwise the return is 97%, which seems too high for a max $5 side bet). Pays are on a "for one" basis.
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Three Fire Dragons | 1000 | 1 | 0.000043 | 0.042688 |
| Three Water Dragons | 1000 | 1 | 0.000043 | 0.042688 |
| Three Dragons with Gold Dragon | 200 | 15 | 0.000640 | 0.128063 |
| Three Natural Dragons | 60 | 18 | 0.000768 | 0.046103 |
| Two Dragons | 7 | 966 | 0.041236 | 0.288654 |
| One Gold Dragon | 5 | 1,035 | 0.044182 | 0.220908 |
| All other | 0 | 21,390 | 0.913088 | 0.000000 |
| Total | 23,426 | 1.000000 | 0.769103 |
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 29th, 2018 at 2:42:31 PM
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Quote: Wizard
3 Fire Dragons
3 Water Dragons
1 wild Gold Dragon
7 Phoenixes (what is the plural of phoenix?)
8 Tigers
9 Pandas
10 Monkeys
12 Rabbits
And a partridge in a pear tree.
Seriously, what's up with these new games that require goofy custom decks?
Casinos are not your friends, they want your money. But so does Disneyland.
And there is no chance in hell that you will go to Disneyland and come back with more money than you went with.
- AxelWolf and Mickeycrimm
September 29th, 2018 at 2:45:34 PM
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Quote: DeucekiesSeriously, what's up with these new games that require goofy custom decks?
I'm assuming they're trying to appeal to younger crowds who grew up with collectible card games and video games and all that kind of jazz.
September 29th, 2018 at 4:44:30 PM
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Quote: TigerWuI'm assuming they're trying to appeal to younger crowds who grew up with collectible card games and video games and all that kind of jazz.
I think anybody alive can remember baseball cards. As for me, I was big on Wacky Packs and Charlie's Angels Cards. With I still had them -- my brother stole many and the mother threw away the rest.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 29th, 2018 at 5:20:59 PM
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Isn't this what Bill Cosby used to do?
Drag and poke her :)
Tip your waitstaff
Drag and poke her :)
Tip your waitstaff
September 29th, 2018 at 6:18:48 PM
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I played a couple hundred hands. It was a steady drain, and the occasional odds pay didn't make up for it. I was never ahead of the original stake.
I think phoenix/panda is too optimistic. I played dragon/tiger or fold, did not fold a single winner, lost several good hands.
Moved to dragon/panda 2nd hundred cards, folded 3 winners, two phoenix high. Lost 6 dragon/panda, 2 dragon/tiger to better non-pair hands.
Easily could be variance, and if the math says phoenix/panda, that's what it says. But just because the preponderance of the cards are panda or lower doesn't seem to mean the dealer will get them.
I think phoenix/panda is too optimistic. I played dragon/tiger or fold, did not fold a single winner, lost several good hands.
Moved to dragon/panda 2nd hundred cards, folded 3 winners, two phoenix high. Lost 6 dragon/panda, 2 dragon/tiger to better non-pair hands.
Easily could be variance, and if the math says phoenix/panda, that's what it says. But just because the preponderance of the cards are panda or lower doesn't seem to mean the dealer will get them.
If the House lost every hand, they wouldn't deal the game.
September 29th, 2018 at 7:05:36 PM
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Quote: DeucekiesSeriously, what's up with these new games that require goofy custom decks?
One reason may be that the Smith decision expressly stated one example of patentable material being a custom deck of cards. Anyone with an idea that uses them has a better chance at patent issuence than others.
Not saying that is definitely the reason, but I’m sure it’s a factor.
.
September 29th, 2018 at 7:38:27 PM
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Quote: mrsuit31Not saying that is definitely the reason, but I’m sure it’s a factor.
I think it's a factor too.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 30th, 2018 at 1:16:53 PM
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In trying to program this game, I realize there is a rule I am not sure about. Who would win in the following situation:
Player: Fire dragon, Fire dragon, Water dragon
Dealer: Panda, Panda, Panda
I welcome your interpretation of the rules in this situation.
Player: Fire dragon, Fire dragon, Water dragon
Dealer: Panda, Panda, Panda
I welcome your interpretation of the rules in this situation.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 30th, 2018 at 2:02:48 PM
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What is the source of the house advantage on the play bet? Does the dealer's hand need to qualify? Also, do ties go to the dealer?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
September 30th, 2018 at 2:15:19 PM
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Quote: WizardIn trying to program this game, I realize there is a rule I am not sure about. Who would win in the following situation:
Player: Fire dragon, Fire dragon, Water dragon
Dealer: Panda, Panda, Panda
I welcome your interpretation of the rules in this situation.
Def. Player. Dragons are dragons and the highest 3OAK regardless of suit/color/wild.
If the House lost every hand, they wouldn't deal the game.
September 30th, 2018 at 2:17:48 PM
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Quote: gordonm888What is the source of the house advantage on the play bet? Does the dealer's hand need to qualify? Also, do ties go to the dealer?
No HA on play except
1. You have to bet/fold first.
2. Mandatory blind bet only pays on panda pair or better, and ONLY if you win. Felt and instructions don't say this. If your panda pair loses to tiger pair, no blind pay.
But if you lose, you lose all 3 bets.
Dealer always qualifies.
Ties push.
If the House lost every hand, they wouldn't deal the game.
September 30th, 2018 at 2:27:12 PM
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I've played another 300 hands today. I strictly played their recommended strategy of phoenix/panda or better. I lost the first 25 times I played this (phoenix /panda or phoenix /tiger). I finally won 1, and it was phoenix/tiger. Lost any subsequent.
I also only played Dragon /panda or better with a dragon in the hand. I folded dragon/monkey/rabbit. That was correct 32 times in a row, then 2 in a row would have won.
I did not ever fold a winner otherwise, and went 250 hands without winning a phoenix top, then won 1 within the last 50. I did push panda/monkey/rabbit twice. I would have expected that more often, actually.
So, I think their OS is incorrect. I think dragon/panda or better is going to be mathematically correct, but I'll be very interested to see what you guys find by the numbers.
I also only played Dragon /panda or better with a dragon in the hand. I folded dragon/monkey/rabbit. That was correct 32 times in a row, then 2 in a row would have won.
I did not ever fold a winner otherwise, and went 250 hands without winning a phoenix top, then won 1 within the last 50. I did push panda/monkey/rabbit twice. I would have expected that more often, actually.
So, I think their OS is incorrect. I think dragon/panda or better is going to be mathematically correct, but I'll be very interested to see what you guys find by the numbers.
If the House lost every hand, they wouldn't deal the game.
September 30th, 2018 at 2:50:44 PM
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Quote: beachbumbabsDef. Player. Dragons are dragons and the highest 3OAK regardless of suit/color/wild.
Then why two different colors of dragons? Who would win here:
Player: Fire dragon, Fire dragon, Fire dragon
Dealer: Water dragon, Water dragon, Water dragon
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 30th, 2018 at 3:33:09 PM
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Side betsQuote: WizardThen why two different colors of dragons? Who would win here:
Quote:
Player: Fire dragon, Fire dragon, Fire dragon
Dealer: Water dragon, Water dragon, Water dragon
Tie.
“Man Babes” #AxelFabulous
September 30th, 2018 at 3:57:07 PM
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Quote: WizardThen why two different colors of dragons? Who would win here:
Player: Fire dragon, Fire dragon, Fire dragon
Dealer: Water dragon, Water dragon, Water dragon
Speculating, so they could build the dragon bonus bet. No other reason I can see. But they differentiate several combos of dragons.
Just like any 7s purple 7s, red 7s on those 3 reel 20 line things. (Can't think of the name. Very popular IGT that awards 12 free spins if you get 3 spin symbols anywhere on the screen. Has cherries and 1,2,3 bars also. Triple double wilds.)
There seem to be equal numbers of purple and red 7s in that game, but the pay on each is different. Think it's arbitrary to build the return they want.
Anyway, I did have pair of blues panda and the board had pair of reds panda, and it was a tie.
If the House lost every hand, they wouldn't deal the game.
September 30th, 2018 at 4:00:07 PM
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Assuming Babs and Miplet are right about the rules, which seems logical, then here are my results of the base game.
I find the advice given in the help files of raising on phoenix-panda-rabbit or better to be correct.
The house edge, measured as the ratio of the expected loss to the Ante bet only, is 3.70%, as shown in the table above.
The player will raise 81% of the time, for an average final wager of 2.8094425. The element of risk is thus 1.32%.
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win with three dragons | 22 | 685,860 | 0.001494 | 0.032863 |
| Win with three phoenixes | 9 | 1,095,395 | 0.002386 | 0.021471 |
| Win with other three of a kind | 6 | 12,597,063 | 0.027436 | 0.164614 |
| With with pair of pandas or better | 3 | 90,652,512 | 0.197436 | 0.592307 |
| Other win | 2 | 113,820,564 | 0.247894 | 0.495789 |
| Push | 0 | 5,423,068 | 0.011811 | 0.000000 |
| Fold | -2 | 87,494,400 | 0.190558 | -0.381115 |
| Loss | -3 | 147,380,738 | 0.320986 | -0.962959 |
| Total | 459,149,600 | 1.000000 | -0.037030 |
I find the advice given in the help files of raising on phoenix-panda-rabbit or better to be correct.
The house edge, measured as the ratio of the expected loss to the Ante bet only, is 3.70%, as shown in the table above.
The player will raise 81% of the time, for an average final wager of 2.8094425. The element of risk is thus 1.32%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 1st, 2018 at 6:28:25 AM
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My WoO page on Dragon Poker is up.
As always, I welcome all questions, comments, and corrections.
As always, I welcome all questions, comments, and corrections.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 1st, 2018 at 7:40:26 AM
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I played the practice game and my experience was same as BBB. A lot of losing.
I like my games to have a little more strategy.
I like my games to have a little more strategy.
October 1st, 2018 at 9:33:11 AM
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Quote: FinsRuleI played the practice game and my experience was same as BBB. A lot of losing.
I like my games to have a little more strategy.
To play the devil's advocate, the structure and experience in this game mimics that of Three Card Poker, and that game made out pretty well.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 1st, 2018 at 9:38:07 AM
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I have played the practice game for a while. It is too simple for my taste. It is like three card poker with:
- more frequent pairing
- no straights or flushes
- one wild card (that can only pair)
- less frequent folding
- more bonus payout hands
Like 3CP, it has one dumb-cluck decision. Overall, it is boring.
- more frequent pairing
- no straights or flushes
- one wild card (that can only pair)
- less frequent folding
- more bonus payout hands
Like 3CP, it has one dumb-cluck decision. Overall, it is boring.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 1st, 2018 at 10:06:15 AM
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I'm going to try to play it at the Rio when I get half a chance to go out that way. As was said earlier, I think it is easier to protect a game, intellectually, with unique cards or other equipment. I don't like jokers though. Had they consulted me, I'd have recommended against it. Plus the thing about Fire and Water Dragons is rather confusing.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 1st, 2018 at 1:34:28 PM
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Quote: WizardTo play the devil's advocate, the structure and experience in this game mimics that of Three Card Poker, and that game made out pretty well.
I agree, but I don’t like playing 3 card for more than 10 minutes either.
I dont think most people enjoy learning new games, so I am kinda bearish on this.
I like Pai Gow poker and tiles.
My ultimate game would be Pai Gow Draw poker, but I don’t have the time or energy to sell it to casinos.
October 1st, 2018 at 1:44:07 PM
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Quote: FinsRuleI like Pai Gow ... tiles.
I think that is all you need to say. I prefer the thinking games too.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 1st, 2018 at 3:46:06 PM
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Thanks Wizard for the analysis of Dragon Poker. The Dragon Bonus payouts is "to 1" instead of "for 1" (the bet stays on the layout) so the HA is more around 15% instead of 24%.
October 1st, 2018 at 3:57:08 PM
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Quote: Settle813Thanks Wizard for the analysis of Dragon Poker. The Dragon Bonus payouts is "to 1" instead of "for 1" (the bet stays on the layout) so the HA is more around 15% instead of 24%.
You're welcome. Thank you for that correction. I played until I had a winning Tiger Bonus hand and can confirm that you're right.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 4th, 2018 at 5:18:21 AM
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Normal cards, I'm conservative
October 4th, 2018 at 8:22:59 AM
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It turns out that Dragon Poker has a small number of possible hands, so its practical to list all the hands and their probabilities and EVs.
In the tables below the hand ID uses this obvious code:
7 = Wild card
6 = Dragon
5 = Phoenix
4 = Tiger
3 = Panda
2 = Monkey
1 = Rabbit
So the lowest possible hand is 321 which is Panda-Monkey-Rabbit. The hand 446 means a pair of Tigers with a Dragon Kicker.
First table is all the hands without a wild card, the 2nd table is all the hands with a wild card. The column labeled EV refers to expected value when making the Play Bet.
One interesting feature: a pair of Pandas with a Dragon kicker has a higher EV than a pair of Tigers with a Rabbit kicker.
In the tables below the hand ID uses this obvious code:
7 = Wild card
6 = Dragon
5 = Phoenix
4 = Tiger
3 = Panda
2 = Monkey
1 = Rabbit
So the lowest possible hand is 321 which is Panda-Monkey-Rabbit. The hand 446 means a pair of Tigers with a Dragon Kicker.
First table is all the hands without a wild card, the 2nd table is all the hands with a wild card. The column labeled EV refers to expected value when making the Play Bet.
| Hand | Probability | EV |
|---|---|---|
| 321 | 0.046102621 | -2.87877551 |
| 421 | 0.040980108 | -2.666632653 |
| 431 | 0.036882097 | -2.484795918 |
| 432 | 0.030735081 | -2.338163265 |
| 521 | 0.035857594 | -2.112397959 |
| 531 | 0.032271835 | -1.958979592 |
| 532 | 0.026893196 | -1.837959184 |
| 541 | 0.028686075 | -1.685153061 |
| 542 | 0.023905063 | -1.580663265 |
| 543 | 0.021514556 | -1.486326531 |
| 621 | 0.030735081 | -1.21505102 |
| 631 | 0.027661573 | -1.089795918 |
| 632 | 0.023051311 | -0.993877551 |
| 641 | 0.024588065 | -0.864285714 |
| 642 | 0.020490054 | -0.782142857 |
| 643 | 0.018441048 | -0.706122449 |
| 651 | 0.021514556 | -0.574234694 |
| 652 | 0.017928797 | -0.505867347 |
| 653 | 0.016135917 | -0.441836735 |
| 654 | 0.014343038 | -0.385969388 |
| 112 | 0.028173824 | -0.204591837 |
| 113 | 0.025356442 | -0.104591837 |
| 114 | 0.022539059 | -0.016581633 |
| 115 | 0.019721677 | 0.059438776 |
| 116 | 0.016904294 | 0.123469388 |
| 221 | 0.023051311 | 0.311887755 |
| 223 | 0.017288483 | 0.463367347 |
| 224 | 0.01536754 | 0.51494898 |
| 225 | 0.013446598 | 0.558877551 |
| 226 | 0.011525655 | 0.595153061 |
| 331 | 0.018441048 | 1.5 |
| 332 | 0.01536754 | 1.587857143 |
| 334 | 0.012294032 | 1.738010204 |
| 335 | 0.010757278 | 1.775510204 |
| 336 | 0.009220524 | 1.993469388 |
| 441 | 0.014343038 | 1.966071429 |
| 442 | 0.011952531 | 2.030357143 |
| 443 | 0.010757278 | 2.088673469 |
| 445 | 0.008366772 | 2.209897959 |
| 446 | 0.007171519 | 2.228418367 |
| 551 | 0.010757278 | 2.358826531 |
| 552 | 0.008964399 | 2.402908163 |
| 553 | 0.008067959 | 2.44377551 |
| 554 | 0.007171519 | 2.480357143 |
| 556 | 0.005378639 | 2.57755102 |
| 661 | 0.00768377 | 2.678571429 |
| 662 | 0.006403142 | 2.705816327 |
| 663 | 0.005762828 | 2.732142857 |
| 664 | 0.005122513 | 2.755714286 |
| 665 | 0.004482199 | 2.776530612 |
| 111 | 0.009391275 | 5.734988206 |
| 222 | 0.005122513 | 5.869778912 |
| 333 | 0.003585759 | 5.90371426 |
| 444 | 0.002390506 | 5.94911223 |
| 555 | 0.001494066 | 8.972489789 |
| 666 | 0.000853752 | 21.99491428 |
| Hand | Probability | EV |
|---|---|---|
| 721 | 0.005122513 | 0.495561224 |
| 731 | 0.004610262 | 1.710306122 |
| 732 | 0.003841885 | 1.79877551 |
| 741 | 0.004098011 | 2.13994898 |
| 742 | 0.003415009 | 2.204846939 |
| 743 | 0.003073508 | 2.263469388 |
| 751 | 0.003585759 | 2.478826531 |
| 752 | 0.002988133 | 2.523520408 |
| 753 | 0.00268932 | 2.564693878 |
| 754 | 0.002390506 | 2.601581633 |
| 761 | 0.003073508 | 2.735204082 |
| 762 | 0.002561257 | 2.763061224 |
| 763 | 0.002305131 | 2.789693878 |
| 764 | 0.002049005 | 2.813571429 |
| 765 | 0.00179288 | 2.834693878 |
| 711 | 0.002817382 | 5.801536971 |
| 722 | 0.001920943 | 5.908554422 |
| 733 | 0.001536754 | 5.933333062 |
| 744 | 0.001195253 | 5.965774869 |
| 755 | 0.00089644 | 8.981739475 |
| 766 | 0.000640314 | 21.99494069 |
One interesting feature: a pair of Pandas with a Dragon kicker has a higher EV than a pair of Tigers with a Rabbit kicker.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 4th, 2018 at 10:12:24 AM
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Quote: gordonm888It turns out that Dragon Poker has a small number of possible hands, so its practical to list all the hands and their probabilities and EVs.
In the tables below the hand ID uses this obvious code:
7 = Wild card
6 = Dragon
5 = Phoenix
4 = Tiger
3 = Panda
2 = Monkey
1 = Rabbit
So the lowest possible hand is 321 which is Panda-Monkey-Rabbit. The hand 446 means a pair of Tigers with a Dragon Kicker.
First table is all the hands without a wild card, the 2nd table is all the hands with a wild card. The column labeled EV refers to expected value when making the Play Bet.
One interesting feature: a pair of Pandas with a Dragon kicker has a higher EV than a pair of Tigers with a Rabbit kicker.
So you're saying only 18.2% of the time a hand should be folded, and any ev better than -2.0 should be played, is that correct? Thanks.
If the House lost every hand, they wouldn't deal the game.
October 4th, 2018 at 10:31:39 AM
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Quote: beachbumbabsSo you're saying only 18.2% of the time a hand should be folded, and any ev better than -2.0 should be played, is that correct? Thanks.
I can't speak for Gordon, but I show the player should fold 19.1% of the time. Yes, any EV less than -2 and the player should fold. Better to lose 2 than more than 2.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 4th, 2018 at 10:39:54 AM
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Gordon, I took the product of your probabilities and the great of the EV and -2. The sum, which should be the EV of the whole game, was -0.035407203.
I'm not saying you're wrong, of course. As you know, my results get -0.037030. Off hand, can you think of anything that may be causing the disparity?
I'm not saying you're wrong, of course. As you know, my results get -0.037030. Off hand, can you think of anything that may be causing the disparity?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 4th, 2018 at 10:55:16 AM
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Quote: WizardI can't speak for Gordon, but I show the player should fold 19.1% of the time. Yes, any EV less than -2 and the player should fold. Better to lose 2 than more than 2.
When I sum the probability of the 5 lowest ranking hands in my table above I get 19.05575% -and those are the 5 hands with EV< - 2.0 that should be folded.
So, I am speculating that there is no disagreement.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 4th, 2018 at 11:02:38 AM
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Quote: WizardGordon, I took the product of your probabilities and the great of the EV and -2. The sum, which should be the EV of the whole game, was -0.035407203.
I'm not saying you're wrong, of course. As you know, my results get -0.037030. Off hand, can you think of anything that may be causing the disparity?
I agree, I also get -0.035407203. My probabilities do sum to exactly 1 for the player hands, so if I have an error it is in my calculation of dealer's hand probabilities or maybe I missed something in applying the payout table. I need some time to check.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 4th, 2018 at 11:27:16 AM
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Quote: gordonm888I agree, I also get -0.035407203. My probabilities do sum to exactly 1 for the player hands, so if I have an error it is in my calculation of dealer's hand probabilities or maybe I missed something in applying the payout table. I need some time to check.
Thanks for checking. If you stand by your figure, I can do a similar table to yours to get the EV of each player hand. Hopefully that will narrow down our point of departure.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 4th, 2018 at 12:40:16 PM
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I found a tiny error with my calculation of Ties for 222 (Trip Monkeys) which I have corrected changing my EV to -0.03556878.
I have listed the probability that I calculate for various payout levels in the last column of the table, below. SO, compare the last two columns to see where our discrepancies are.
Some problem with Win and Tie and Lose on Payout=3 hands (pairs that are panda-panda or higher.)
That's as far as I have gotten. I wonder if our discrepancy arises from how we treat dealer hands involving a wild card that count as a pair (e.g., 761) when calculating win-tie-loss for Payout 3 hands.
I have listed the probability that I calculate for various payout levels in the last column of the table, below. SO, compare the last two columns to see where our discrepancies are.
Some problem with Win and Tie and Lose on Payout=3 hands (pairs that are panda-panda or higher.)
| Event | Pays | WOO Combinations | WOO Probability | Gordon's Probability |
|---|---|---|---|---|
| Win with three dragons | 22 | 685,860 | 0.001494 | 0.001494 |
| Win with three phoenixes | 9 | 1,095,395 | 0.002386 | 0.002386 |
| Win with other three of a kind | 6 | 12,597,063 | 0.027436 | 0.027436 |
| With with pair of pandas or better | 3 | 90,652,512 | 0.197436 | 0.197719 |
| Other win | 2 | 113,820,564 | 0.247894 | 0.247894 |
| Push | 0 | 5,423,068 | 0.011811 | 0.011731 |
| Fold | -2 | 87,494,400 | 0.190558 | 0.190558 |
| Loss | -3 | 147,380,738 | 0.320986 | 0.320782 |
| Total | 459,149,600 | 1.000000 | 1.0000 |
That's as far as I have gotten. I wonder if our discrepancy arises from how we treat dealer hands involving a wild card that count as a pair (e.g., 761) when calculating win-tie-loss for Payout 3 hands.
Last edited by: gordonm888 on Oct 4, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 4th, 2018 at 1:29:33 PM
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Thank you for that table and looking into this. I double checked my code and don't immediately see a problem with how I'm scoring hands like that. Here is the code, if you're interested. I sort from lowest to highest and the card with a value of 6 is the wild card. It returns a score for the hand.
Our difference is rather small. What I think I'll do is look for the In Bet guys at the show next week and see if I can peek or have their math report, which will give us a third opinion.
int score(int c[])
{
if (c[2]!=6) // no wild card
{
if (c[0]==c[2]) // three of a kind
return 2000+c[0];
else if (c[0]==c[1]) // pair
return 1000+10*c[1]+c[2];
else if (c[2]==c[1]) // pair
return 1000+10*c[1]+c[0];
else
return 100*c[2]+10*c[1]+c[0];
}
else // wild card
{
if (c[1]==c[0]) // three of a kind
return 2000+c[1];
else
return 1000+10*c[1]+c[0];
}
}
Our difference is rather small. What I think I'll do is look for the In Bet guys at the show next week and see if I can peek or have their math report, which will give us a third opinion.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 4th, 2018 at 4:50:21 PM
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I agree with Wizard’s analyses.
gordonm888:
You should get the same EV with 3 dragons. You list 2 different EV's depending on if they are using a wild.
gordonm888:
You should get the same EV with 3 dragons. You list 2 different EV's depending on if they are using a wild.
| Hand | Pays | Ways | EV |
|---|---|---|---|
| win | 22 | 19596 | 21.9955102 |
| tie | 0 | 4 | 0 |
| Total | 19600 | 21.9955102 |
“Man Babes” #AxelFabulous
October 4th, 2018 at 5:40:07 PM
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Quote: mipletI agree with Wizard’s analyses.
gordonm888:
You should get the same EV with 3 dragons. You list 2 different EV's depending on if they are using a wild.
Hand Pays Ways EV win 22 19596 21.9955102 tie 0 4 0 Total 19600 21.9955102
Yes, I agree with your point on 3 dragons. Since posting that table, I had already noticed this "3 Dragons discrepancy" and I had found an error in my formula for the probability of Tieing with trips. Correcting that error caused my calculated EV value to move even further away from Wiz's results.
I accept that Wiz's and your analysis is correct, and that mine has an error in it. My spreadsheet is completely different than a looping code- the input/starting point is the composition of the starting deck of cards, and it is essentially a 77 x 77 matrix that immediately calculates the Dealer's probability of all 77 possible hands/outcomes for each of the player's 77 starting hands. Thus, the Total EV/HE and the EV for every possible player hand is calculated instantly for any specified "deck composition." As such, it just seems natural that I would have something awry somewhere within the 77x77 cells. However, given 53 starting cards the combinations in the 77x77 cells do all sum to 459,149,600 and the nature of my error has proved to be elusive. I'll probably wake up at 5:00 a.m. tomorrow morning with the sudden realization of what the error is, but right now I'm stumped.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 4th, 2018 at 7:58:48 PM
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Thank you Miplet for the third opinion.
That happens to me often. I get my best ideas when I let my brain go on a free flow of thoughts. If I'm staring at computer code, I can't see an obvious error right in front of my nose.
This happened with Casino Dominoes. I was out riding my unicycle, letting my mind wander, and realized a mistake in my code.
Quote: gordonm888I'll probably wake up at 5:00 a.m. tomorrow morning with the sudden realization of what the error is, but right now I'm stumped.
That happens to me often. I get my best ideas when I let my brain go on a free flow of thoughts. If I'm staring at computer code, I can't see an obvious error right in front of my nose.
This happened with Casino Dominoes. I was out riding my unicycle, letting my mind wander, and realized a mistake in my code.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 5th, 2018 at 6:58:43 AM
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LOL, the revelation happened at 8:30 am -which is 5:30 am in Vegas. I now calculate 3.703041%.
I had a single data entry issue on one single hand - Panda-Panda-Dragon -which essentially removed 2 pandas and the wild card (rather than 2 pandas and a dragon) from the deck when calculating dealer outcome probabilities for that one player hand. And I had used manual data entry rather than algorithms to generate the data in this field because there were so few hands to characterize - hence the possibility of a human error.
For the record, here are the corrected tables of probability and EV for every Dragon Poker Hand.
**************************************************************************
In the tables below the hand ID uses this code:
7 = Wild card
6 = Dragon
5 = Phoenix
4 = Tiger
3 = Panda
2 = Monkey
1 = Rabbit
So the lowest possible hand is 321 which is Panda-Monkey-Rabbit. The hand 446 means a pair of Tigers with a Dragon Kicker.
First table is all the hands without a wild card, the 2nd table is all the hands with a wild card. The column labeled EV refers to expected value when making the Play Bet.
I had a single data entry issue on one single hand - Panda-Panda-Dragon -which essentially removed 2 pandas and the wild card (rather than 2 pandas and a dragon) from the deck when calculating dealer outcome probabilities for that one player hand. And I had used manual data entry rather than algorithms to generate the data in this field because there were so few hands to characterize - hence the possibility of a human error.
For the record, here are the corrected tables of probability and EV for every Dragon Poker Hand.
**************************************************************************
In the tables below the hand ID uses this code:
7 = Wild card
6 = Dragon
5 = Phoenix
4 = Tiger
3 = Panda
2 = Monkey
1 = Rabbit
So the lowest possible hand is 321 which is Panda-Monkey-Rabbit. The hand 446 means a pair of Tigers with a Dragon Kicker.
First table is all the hands without a wild card, the 2nd table is all the hands with a wild card. The column labeled EV refers to expected value when making the Play Bet.
| Hand | Probability | EV |
|---|---|---|
| 321 | 0.046102621 | -2.87877551 |
| 421 | 0.040980108 | -2.666632653 |
| 431 | 0.036882097 | -2.484795918 |
| 432 | 0.030735081 | -2.338163265 |
| 521 | 0.035857594 | -2.112397959 |
| 531 | 0.032271835 | -1.958979592 |
| 532 | 0.026893196 | -1.837959184 |
| 541 | 0.028686075 | -1.685153061 |
| 542 | 0.023905063 | -1.580663265 |
| 543 | 0.021514556 | -1.486326531 |
| 621 | 0.030735081 | -1.21505102 |
| 631 | 0.027661573 | -1.089795918 |
| 632 | 0.023051311 | -0.993877551 |
| 641 | 0.024588065 | -0.864285714 |
| 642 | 0.020490054 | -0.782142857 |
| 643 | 0.018441048 | -0.706122449 |
| 651 | 0.021514556 | -0.574234694 |
| 652 | 0.017928797 | -0.505867347 |
| 653 | 0.016135917 | -0.441836735 |
| 654 | 0.014343038 | -0.385969388 |
| 112 | 0.028173824 | -0.204591837 |
| 113 | 0.025356442 | -0.104591837 |
| 114 | 0.022539059 | -0.016581633 |
| 115 | 0.019721677 | 0.059438776 |
| 116 | 0.016904294 | 0.123469388 |
| 221 | 0.023051311 | 0.311887755 |
| 223 | 0.017288483 | 0.463367347 |
| 224 | 0.01536754 | 0.51494898 |
| 225 | 0.013446598 | 0.558877551 |
| 226 | 0.011525655 | 0.595153061 |
| 331 | 0.018441048 | 1.5 |
| 332 | 0.01536754 | 1.587857143 |
| 334 | 0.012294032 | 1.738010204 |
| 335 | 0.010757278 | 1.775510204 |
| 336 | 0.009220524 | 1.805969388 |
| 441 | 0.014343038 | 1.966071429 |
| 442 | 0.011952531 | 2.030357143 |
| 443 | 0.010757278 | 2.088673469 |
| 445 | 0.008366772 | 2.209897959 |
| 446 | 0.007171519 | 2.228418367 |
| 551 | 0.010757278 | 2.358826531 |
| 552 | 0.008964399 | 2.402908163 |
| 553 | 0.008067959 | 2.44377551 |
| 554 | 0.007171519 | 2.480357143 |
| 556 | 0.005378639 | 2.57755102 |
| 661 | 0.00768377 | 2.678571429 |
| 662 | 0.006403142 | 2.705816327 |
| 663 | 0.005762828 | 2.732142857 |
| 664 | 0.005122513 | 2.755714286 |
| 665 | 0.004482199 | 2.776530612 |
| 111 | 0.009391275 | 5.752040816 |
| 222 | 0.005122513 | 5.847397959 |
| 333 | 0.003585759 | 5.908928571 |
| 444 | 0.002390506 | 5.952091837 |
| 555 | 0.001494066 | 8.973979592 |
| 666 | 0.000853752 | 21.9955102 |
| Hand | Probability | EV |
|---|---|---|
| 721 | 0.005122513 | 0.495561224 |
| 731 | 0.004610262 | 1.710306122 |
| 732 | 0.003841885 | 1.79877551 |
| 741 | 0.004098011 | 2.13994898 |
| 742 | 0.003415009 | 2.204846939 |
| 743 | 0.003073508 | 2.263469388 |
| 751 | 0.003585759 | 2.478826531 |
| 752 | 0.002988133 | 2.523520408 |
| 753 | 0.00268932 | 2.564693878 |
| 754 | 0.002390506 | 2.601581633 |
| 761 | 0.003073508 | 2.735204082 |
| 762 | 0.002561257 | 2.763061224 |
| 763 | 0.002305131 | 2.789693878 |
| 764 | 0.002049005 | 2.813571429 |
| 765 | 0.00179288 | 2.834693878 |
| 711 | 0.002817382 | 5.818622449 |
| 722 | 0.001920943 | 5.893316327 |
| 733 | 0.001536754 | 5.938316327 |
| 744 | 0.001195253 | 5.968622449 |
| 755 | 0.00089644 | 8.983163265 |
| 766 | 0.000640314 | 21.9955102 |
Last edited by: gordonm888 on Oct 5, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 5th, 2018 at 9:01:54 AM
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I get the 3.703041% but interestingly (when I had a bug in the code) got 1.297% if there was a bonus for any pair. Also if you had 3 decks the HE=.103%, with more decks the player gets an advantage (because it's easier to make good hands).
I used a pack of cards - using a generic coding that could cater for other pack distributions! So a Joker is Wild and Ace = any Dragon etc.
I used a pack of cards - using a generic coding that could cater for other pack distributions! So a Joker is Wild and Ace = any Dragon etc.
| * A A | 117 576 | 24 | 0 | 21.995 510 |
| * A K | 114 180 | 360 | 3 060 | 2.834 694 |
| * A Q | 113 736 | 420 | 3 444 | 2.813 571 |
| * A J | 113 238 | 480 | 3 882 | 2.789 694 |
| * A T | 112 686 | 540 | 4 374 | 2.763 061 |
| * A 9 | 112 080 | 660 | 4 860 | 2.735 204 |
| * K K | 117 420 | 60 | 120 | 8.983 163 |
| * K Q | 109 476 | 630 | 7 494 | 2.601 582 |
| * K J | 108 708 | 720 | 8 172 | 2.564 694 |
| * K T | 107 856 | 810 | 8 934 | 2.523 520 |
| * K 9 | 106 890 | 990 | 9 720 | 2.478 827 |
| * Q Q | 117 150 | 120 | 330 | 5.968 622 |
| * Q J | 102 660 | 1 008 | 13 932 | 2.263 469 |
| * Q T | 101 448 | 1 134 | 15 018 | 2.204 847 |
| * Q 9 | 100 050 | 1 386 | 16 164 | 2.139 949 |
| * J J | 116 724 | 210 | 666 | 5.938 316 |
| * J T | 93 300 | 1 512 | 22 788 | 1.798 776 |
| * J 9 | 91 398 | 1 848 | 24 354 | 1.710 306 |
| * T T | 116 094 | 336 | 1 170 | 5.893 316 |
| * T 9 | 80 790 | 2 376 | 34 434 | 0.495 561 |
| * 9 9 | 114 990 | 720 | 1 890 | 5.818 622 |
| A A A | 117 576 | 24 | 0 | 21.995 510 |
| A A K | 113 040 | 360 | 4 200 | 2.776 531 |
| A A Q | 112 602 | 420 | 4 578 | 2.755 714 |
| A A J | 112 110 | 480 | 5 010 | 2.732 143 |
| A A T | 111 564 | 540 | 5 496 | 2.705 816 |
| A A 9 | 110 970 | 660 | 5 970 | 2.678 571 |
| A K K | 109 170 | 300 | 8 130 | 2.577 551 |
| A K Q | 60 726 | 1 260 | 55 614 | -0.385 969 |
| A K J | 59 304 | 1 440 | 56 856 | -0.441 837 |
| A K T | 57 690 | 1 620 | 58 290 | -0.505 867 |
| A K 9 | 55 866 | 1 980 | 59 754 | -0.574 235 |
| A Q Q | 102 252 | 450 | 14 898 | 2.228 418 |
| A Q J | 52 944 | 1 680 | 62 976 | -0.706 122 |
| A Q T | 51 030 | 1 890 | 64 680 | -0.782 143 |
| A Q 9 | 48 846 | 2 310 | 66 444 | -0.864 286 |
| A J J | 93 882 | 630 | 23 088 | 1.805 969 |
| A J T | 45 888 | 2 160 | 69 552 | -0.993 878 |
| A J 9 | 43 344 | 2 640 | 71 616 | -1.089 796 |
| A T T | 84 054 | 840 | 32 706 | 0.595 153 |
| A T 9 | 40 200 | 2 970 | 74 430 | -1.215 051 |
| A 9 9 | 72 654 | 1 350 | 43 596 | 0.123 469 |
| K K K | 117 330 | 60 | 210 | 8.973 980 |
| K K Q | 107 100 | 630 | 9 870 | 2.480 357 |
| K K J | 106 338 | 720 | 10 542 | 2.443 776 |
| K K T | 105 492 | 810 | 11 298 | 2.402 908 |
| K K 9 | 104 538 | 990 | 12 072 | 2.358 827 |
| K Q Q | 101 844 | 540 | 15 216 | 2.209 898 |
| K Q J | 34 392 | 2 016 | 81 192 | -1.486 327 |
| K Q T | 32 022 | 2 268 | 83 310 | -1.580 663 |
| K Q 9 | 29 262 | 2 772 | 85 566 | -1.685 153 |
| K J J | 93 222 | 756 | 23 622 | 1.775 510 |
| K J T | 25 776 | 2 592 | 89 232 | -1.837 959 |
| K J 9 | 22 584 | 3 168 | 91 848 | -1.958 980 |
| K T T | 83 100 | 1 008 | 33 492 | 0.558 878 |
| K T 9 | 18 738 | 3 564 | 95 298 | -2.112 398 |
| K 9 9 | 70 986 | 1 620 | 44 994 | 0.059 439 |
| Q Q Q | 116 934 | 120 | 546 | 5.952 092 |
| Q Q J | 99 234 | 1 008 | 17 358 | 2.088 673 |
| Q Q T | 98 028 | 1 134 | 18 438 | 2.030 357 |
| Q Q 9 | 96 642 | 1 386 | 19 572 | 1.966 071 |
| Q J J | 92 424 | 882 | 24 294 | 1.738 010 |
| Q J T | 13 752 | 3 024 | 100 824 | -2.338 163 |
| Q J 9 | 9 900 | 3 696 | 104 004 | -2.484 796 |
| Q T T | 81 966 | 1 176 | 34 458 | 0.514 949 |
| Q T 9 | 5 346 | 4 158 | 108 096 | -2.666 633 |
| Q 9 9 | 69 036 | 1 890 | 46 674 | -0.016 582 |
| J J J | 116 340 | 210 | 1 050 | 5.908 929 |
| J J T | 89 166 | 1 512 | 26 922 | 1.587 857 |
| J J 9 | 87 276 | 1 848 | 28 476 | 1.500 000 |
| J T T | 80 652 | 1 344 | 35 604 | 0.463 367 |
| J T 9 | 0 | 4 752 | 112 848 | -2.878 776 |
| J 9 9 | 66 804 | 2 160 | 48 636 | -0.104 592 |
| T T T | 115 494 | 336 | 1 770 | 5.847 398 |
| T T 9 | 76 470 | 2 376 | 38 754 | 0.311 888 |
| T 9 9 | 64 290 | 2 430 | 50 880 | -0.204 592 |
| 9 9 9 | 114 120 | 720 | 2 760 | 5.752 041 |
October 5th, 2018 at 9:46:02 AM
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I did over a dozen spot checks and my results and Charlies appear to be identical.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 5th, 2018 at 11:03:43 AM
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Quote: gordonm888I did over a dozen spot checks and my results and Charlies appear to be identical.
I checked everything in both and they agree with my numbers.
“Man Babes” #AxelFabulous
October 5th, 2018 at 3:19:38 PM
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this game seems to be targeting one gambling group in particular.Quote: Wizardbut played with a modified deck, as follows, in rank order, from highest to lowest:
3 Fire Dragons
3 Water Dragons
1 wild Gold Dragon
7 Phoenixes (what is the plural of phoenix?)
8 Tigers
9 Pandas
10 Monkeys
12 Rabbits
does anyone really think this can fly in a casino?
who can follow if from a surveillance viewpoint?
I can understand Casino War
My Mom looked at the game this passed weekend, and that is all she said.
Sally
I Heart Vi Hart
October 6th, 2018 at 8:17:00 AM
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Okay, let's have some fun.
Importance of the Wild Card
Hands with a Wild: Avg EV = + 2.986
Hands with no Wild : Avg EV = - 0.2184
Of course, that's an aspect of poker games with a Wild Card: the entire game seems to revolve around whether or not you have the wild card.
Effect of Removal
Here are the EOR's or Effect of Removal. These assume that both hands are unknown and that one card of the given rank is removed from the 53-card deck.
These EORs are driven by whether the absence of the card increases or decreases the frequency with which player will get the high payout hands (trips and high pairs.)
Importance of the Wild Card
Hands with a Wild: Avg EV = + 2.986
Hands with no Wild : Avg EV = - 0.2184
Of course, that's an aspect of poker games with a Wild Card: the entire game seems to revolve around whether or not you have the wild card.
Effect of Removal
Here are the EOR's or Effect of Removal. These assume that both hands are unknown and that one card of the given rank is removed from the 53-card deck.
| Card Removed | Player EV,% | EOR,% |
|---|---|---|
| None | -3.703 | 0 |
| Wild | -10.044 | -6.341 |
| Dragon | -4.316 | -0.613 |
| Phoenix | -3.714 | -0.011 |
| Tiger | -3.678 | 0.026 |
| Panda | -3.902 | -0.199 |
| Monkey | -2.983 | 0.720 |
| Rabbit | -3.330 | 0.373 |
These EORs are driven by whether the absence of the card increases or decreases the frequency with which player will get the high payout hands (trips and high pairs.)
Last edited by: gordonm888 on Oct 6, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
