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

Wizard
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September 29th, 2018 at 1:13:23 PM permalink
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?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
TigerWu
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September 29th, 2018 at 1:19:31 PM permalink
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.
Wizard
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September 29th, 2018 at 1:26:51 PM permalink
Quote: TigerWu

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.



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)
Wizard
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September 29th, 2018 at 2:01:35 PM permalink
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)
Wizard
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September 29th, 2018 at 2:10:43 PM permalink
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)
Deucekies
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September 29th, 2018 at 2:42:31 PM permalink
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
TigerWu
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September 29th, 2018 at 2:45:34 PM permalink
Quote: Deucekies

Seriously, 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.
Wizard
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September 29th, 2018 at 4:44:30 PM permalink
Quote: TigerWu

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.



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)
Johnzimbo
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September 29th, 2018 at 5:20:59 PM permalink
Isn't this what Bill Cosby used to do?

Drag and poke her :)

Tip your waitstaff
beachbumbabs
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September 29th, 2018 at 6:18:48 PM permalink
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.
If the House lost every hand, they wouldn't deal the game.
mrsuit31
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September 29th, 2018 at 7:05:36 PM permalink
Quote: Deucekies

Seriously, 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.
.
Wizard
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September 29th, 2018 at 7:38:27 PM permalink
Quote: mrsuit31

Not 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)
Wizard
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September 30th, 2018 at 1:16:53 PM permalink
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
gordonm888
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September 30th, 2018 at 2:02:48 PM permalink
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.
beachbumbabs
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September 30th, 2018 at 2:15:19 PM permalink
Quote: Wizard

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.



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.
beachbumbabs
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September 30th, 2018 at 2:17:48 PM permalink
Quote: gordonm888

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?



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.
beachbumbabs
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September 30th, 2018 at 2:27:12 PM permalink
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.
If the House lost every hand, they wouldn't deal the game.
Wizard
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September 30th, 2018 at 2:50:44 PM permalink
Quote: beachbumbabs

Def. 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)
miplet
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September 30th, 2018 at 3:33:09 PM permalink
Quote: Wizard

Then why two different colors of dragons? Who would win here:

Side bets
Quote:


Player: Fire dragon, Fire dragon, Fire dragon
Dealer: Water dragon, Water dragon, Water dragon


Tie.
“Man Babes” #AxelFabulous
beachbumbabs
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September 30th, 2018 at 3:57:07 PM permalink
Quote: Wizard

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



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.
Wizard
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September 30th, 2018 at 4:00:07 PM permalink
Assuming Babs and Miplet are right about the rules, which seems logical, then here are my results of the base game.

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)
Wizard
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October 1st, 2018 at 6:28:25 AM permalink
My WoO page on Dragon Poker is up.

As always, I welcome all questions, comments, and corrections.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
FinsRule
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October 1st, 2018 at 7:40:26 AM permalink
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.
Wizard
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October 1st, 2018 at 9:33:11 AM permalink
Quote: FinsRule

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.



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)
gordonm888
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October 1st, 2018 at 9:38:07 AM permalink
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.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Wizard
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October 1st, 2018 at 10:06:15 AM permalink
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)
FinsRule
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October 1st, 2018 at 1:34:28 PM permalink
Quote: Wizard

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.



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.
Wizard
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October 1st, 2018 at 1:44:07 PM permalink
Quote: FinsRule

I 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)
Settle813
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October 1st, 2018 at 3:46:06 PM permalink
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%.
Wizard
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October 1st, 2018 at 3:57:08 PM permalink
Quote: Settle813

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%.



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)
IpksiumMaskozis
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October 4th, 2018 at 5:18:21 AM permalink
Normal cards, I'm conservative
gordonm888
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October 4th, 2018 at 8:22:59 AM permalink
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.

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.
beachbumbabs
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October 4th, 2018 at 10:12:24 AM permalink
Quote: gordonm888

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.

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 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.
Wizard
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October 4th, 2018 at 10:31:39 AM permalink
Quote: beachbumbabs

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.



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.
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October 4th, 2018 at 10:39:54 AM permalink
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?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
gordonm888
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October 4th, 2018 at 10:55:16 AM permalink
Quote: Wizard

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.



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.
gordonm888
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October 4th, 2018 at 11:02:38 AM permalink
Quote: Wizard

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 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.
Wizard
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October 4th, 2018 at 11:27:16 AM permalink
Quote: gordonm888

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.



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.
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October 4th, 2018 at 12:40:16 PM permalink
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.)

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.
Wizard
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October 4th, 2018 at 1:29:33 PM permalink
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.


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)
miplet
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October 4th, 2018 at 4:50:21 PM permalink
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.
HandPaysWaysEV
win221959621.9955102
tie040
Total1960021.9955102
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October 4th, 2018 at 5:40:07 PM permalink
Quote: miplet

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.

HandPaysWaysEV
win221959621.9955102
tie040
Total1960021.9955102



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.
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October 4th, 2018 at 7:58:48 PM permalink
Thank you Miplet for the third opinion.

Quote: gordonm888

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.



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.
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October 5th, 2018 at 6:58:43 AM permalink
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.

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.
charliepatrick
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October 5th, 2018 at 9:01:54 AM permalink
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.
* 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
gordonm888
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charliepatrick
October 5th, 2018 at 9:46:02 AM permalink
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.
miplet
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October 5th, 2018 at 11:03:43 AM permalink
Quote: gordonm888

I 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
mustangsally
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October 5th, 2018 at 3:19:38 PM permalink
Quote: Wizard

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

this game seems to be targeting one gambling group in particular.
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
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gordonm888
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October 6th, 2018 at 8:17:00 AM permalink
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.

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.
Gialmere
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January 14th, 2019 at 6:30:43 PM permalink
It's a long shot but does anyone know where to buy a deck for this game? Apart from the Wizard sites no one seems to have heard of it.
Have you tried 22 tonight? I said 22.
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