Poll

 Yes -- I love to try new things. 3 votes (15.78%) Call me maybe. 4 votes (21.05%) No -- I'll stick to normal cards, thank you. 10 votes (52.63%) I'm surprised nobody thought of this name before. 3 votes (15.78%) That plural is phoenices, Wiz. No votes (0%) There is a joke in there somewhere. 2 votes (10.52%) Bring back Flip~it! 1 vote (5.26%) All praise the Flying Spaghetti Monster. 4 votes (21.05%) Total eclipse reminder 04/08/2024 2 votes (10.52%) I need to refresh my knowledge of Leibniz's rule. 3 votes (15.78%)

19 members have voted

Joined: Oct 3, 2018
• Posts: 1
October 4th, 2018 at 5:18:21 AM permalink
Normal cards, I'm conservative
gordonm888
Joined: Feb 18, 2015
• Posts: 3185
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
Joined: May 21, 2013
• Posts: 14232
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

Joined: Oct 14, 2009
• Posts: 23281
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.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard

Joined: Oct 14, 2009
• Posts: 23281
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?
It's not whether you win or lose; it's whether or not you had a good bet.
gordonm888
Joined: Feb 18, 2015
• Posts: 3185
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
Joined: Feb 18, 2015
• Posts: 3185
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

Joined: Oct 14, 2009
• Posts: 23281
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.
It's not whether you win or lose; it's whether or not you had a good bet.
gordonm888
Joined: Feb 18, 2015
• Posts: 3185
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

Joined: Oct 14, 2009
• Posts: 23281
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.
It's not whether you win or lose; it's whether or not you had a good bet.