Super Draw 6 Card Poker

Super Draw 6 Card Poker is a new video poker variant I noticed at VideoPoker.com. The idea is simple -- the player gets a sixth card on the draw. Of course, nothing is ever free. The player must double his bet for this extra card. There are some new six-card hands added to the pay table too.

Example:

Here I'm dealt three deuces.



I hold the three deuces. Of the three hands, one improves to a full house and the other to a four of a kind.



So far I have only done a scoring function. Here is how often each hand occurs in Double Double Bonus, if the game dealt six cards on the deal, which it doesn't. Where two wins are possible, I go with the one that pays more. When two pays are still possible, for example with suited 9TJQKA, it is arbitrary which one I count it as.

That said, here is my score array:

Hand	Pays	Count
Six-card royal flush	1600	4
Six-card straight flush	800	32
Royal flush	800	114
Four of a kind + pair	400	936
Four aces + 2-4	400	480
Four 2-4 + A-4	160	1,440
Four aces + 5-K	160	576
Four 2-4 + 5-K	80	1,728
Straight flush	50	930
Four 5-K + 5-K	50	9,504
Two three of a kind	40	1,248
Six-card flush	25	6,828
Six-card straight	12	36,828
Three pair	9	61,776
Full house	9	164,736
Five-card flush	6	199,080
Five-card straight	4	325,440
Three of a kind	3	732,160
Two pair	1	2,471,040
Jacks or better	1	3,000,756
Nothing	0	13,342,884
Total		20,358,520

The question for the poll is would you play Super Draw 6 Card Poker, given the same return as conventional video poker?

I have and would play this game, though I like several others better (QQ's, HotRoll, SplitPoker to name 3).

I also don't get why anybody likes Rent. But I had to choose only 1 answer.

Went to go try it, but seems that it's the only game in the free list that says you have to be gold.

Something is wrong with your scoring array. Royal flush should be 4 suits * 46 cards that don't make a 6 card Royal.
Others are also off, but I can't check them until I get home.

Quote: miplet

Something is wrong with your scoring array. Royal flush should be 4 suits * 46 cards that don't make a 6 card Royal.
Others are also off, but I can't check them until I get home.

Good catch. I'm working on fixing that.

Okay, here is my new and improved hand count array.

Hand	Pays	Count
Six-card royal flush	1600	4
Six-card straight flush	800	28
Royal flush	800	184
Four of a kind + pair	400	936
Four aces + 2-4	400	480
Four 2-4 + A-4	160	1,440
Four aces + 5-K	160	576
Four 2-4 + 5-K	80	1,728
Straight flush	50	1,444
Four 5-K + 5-K	50	9,504
Two three of a kind	40	1,248
Six-card flush	25	6,608
Six-card straight	12	36,624
Three pair	9	61,776
Full house	9	164,736
Five-card flush	6	198,924
Five-card straight	4	325,440
Three of a kind	3	732,160
Two pair	1	2,471,040
Jacks or better	1	3,000,756
Nothing	0	13,342,884
Total		20,358,520

I previously had some problems scoring hands that could be both straights and flushes, but not necessarily the same cards in each of them.

Here is what I have so far:

Hand	Ways
Six-card royal flush	4
Six-card straight flush	32
Royal flush	184
Four of a kind + pair	936
Four aces + 2-4	480
Four 2-4 + A-4	1440
Four aces + 5-K	576
Four 2-4 + 5-K	1728
Straight flush	1624
Four 5-K	9504
Two three of a kind	1248
Six-card flush
Six-card straight
Three pair	61776
Full house	164736
Five-card flush
Five-card straight
Three of a kind	732160
Two pair
Jacks or better
Nothing

we disagree on 2 of them:
Six-card straight flush: 4 suits * 8 6-card straights (A-6 through 8-K) = 32
Straight flush: 4 suits * 8 5-card straights (2-6 throuh 9-k) * 45 cards that don't make a 6-card straight flush. +
4 suits * 1 (A-5 straight) * 46 cards that don't make a 6-card straight flush
4*8*45+4*1*46=1624

Here is version 3:

Hand	Pays	Count
Six-card royal flush	1600	4
Six-card straight flush	800	32
Five-card Royal flush	800	184
Four of a kind + pair	400	936
Four aces + 2-4	400	480
Four 2-4 + A-4	160	1,440
Four aces + 5-K	160	576
Four 2-4 + 5-K	80	1,728
Five-card straight flush	50	1,624
Four 5-K + 5-K	50	9,504
Two three of a kind	40	1,248
Six-card flush	25	6,580
Six-card straight	12	36,612
Three pair	9	61,776
Full house	9	164,736
Five-card flush	6	198,780
Five-card straight	4	325,440
Three of a kind	3	732,160
Two pair	1	2,471,040
Jacks or better	1	3,000,756
Nothing	0	13,342,884
Total		20,358,520

Looks like we agree on what you have so far.

I have my program up and running for this game. It takes 12.3 hours to work through a pay table so I won't know until tomorrow morning how it's working.

I think my program is working properly. Here are the results for 9-6 Double Double Bonus, which is available at VideoPoker.com. The return column is the product of the win, probability, and 0.5 (because the player must double his bet to pay for the feature). So, 99.32% return.

Hand	Pays	Combinations	Probability	Return
Six-card royal flush	1600	376,189,752	0.000003	0.002157
Six-card straight flush	800	2,286,403,812	0.000016	0.006554
Four of a kind + pair	400	53,862,873,696	0.000386	0.077205
Two three of a kind	40	65,862,044,532	0.000472	0.009440
Six-card flush	25	438,221,653,116	0.003141	0.039258
Six-card straight	12	566,514,956,100	0.004060	0.024361
Three pair	9	1,081,046,587,176	0.007748	0.034864
Five-card Royal flush	800	10,081,123,716	0.000072	0.028900
Five-card straight flush	50	60,590,252,904	0.000434	0.010856
Four aces + 2-4	400	21,304,708,188	0.000153	0.030537
Four 2-4 + A-4	160	55,526,542,512	0.000398	0.031836
Four aces + 5-K	160	24,144,767,196	0.000173	0.013843
Four 2-4 + 5-K	80	63,303,595,992	0.000454	0.018147
Four 5-K + 5-K	50	354,234,143,508	0.002539	0.063468
Full house	9	4,159,440,047,808	0.029810	0.134144
Five-card flush	6	5,523,829,609,812	0.039588	0.118764
Five-card straight	4	3,764,795,765,184	0.026981	0.053963
Three of a kind	3	11,278,297,316,688	0.080829	0.121244
Two pair	1	27,093,903,864,696	0.194176	0.097088
Jacks or better	1	21,377,316,797,196	0.153207	0.076603
Nothing	0	63,537,674,376,816	0.455361	0.000000
Total		139,532,613,620,400	1.000000	0.993233

VideoPoker.com link