Best videopoker bonuses

billryan
billryan
billryan
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December 25th, 2016 at 9:36:55 PM permalink
With a starting hand of three deuces, what are your odds of getting a hand better than four of a kind.
It would be a straight flush, a wild royal or five of a kind, but I'm not sure how to figure the chances of each.
Any help would be appreciated.
The older I get, the better I recall things that never happened
DRich
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December 26th, 2016 at 5:22:01 AM permalink
Wizardofodds.com has a hand analyzer in the video poker section. Choose a deuces game and hold three deuces and two random cards. It will show the probability of each potential hand.
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beachbumbabs
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December 26th, 2016 at 5:32:54 AM permalink
Also 4 deuces, fwiw, among those improved hands the OP listed.
If the House lost every hand, they wouldn't deal the game.
JB
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billryan
December 26th, 2016 at 6:34:57 AM permalink
It depends on the discards. For example, tossing unsuited Ace-Ten can make fewer Wild Royals than tossing 3-8.

Looking at all 3-deuce starting hands (even those which are already better than 4-of-a-kind, except 4 deuces), the probabilities of improving range from 24.05% to 24.7%.

The discards most likely to improve are 33 and KK. (Not necessarily the best EV, just most likely to improve beyond 4-of-a-kind.)
The discards least likely to improve are unsuited 78, 79, 7T, 89, 8T, and 9T.

Interesting observations:
- 3 deuces is more likely to improve to 4 deuces than to a Wild Royal, no matter the discards
- 5 of a kind is more likely when the starting hand was 5 of a kind

Discards 4K SF 5K WR 4W p(>4K)
Pair 33 814 114 67 40 46 24.6994%
Pair 44 816 112 67 40 46 24.5143%
Pair 55 818 110 67 40 46 24.3293%
Pair 66 818 110 67 40 46 24.3293%
Pair 77 820 108 67 40 46 24.1443%
Pair 88 820 108 67 40 46 24.1443%
Pair 99 820 108 67 40 46 24.1443%
Pair TT 820 116 67 32 46 24.1443%
Pair JJ 818 118 67 32 46 24.3293%
Pair QQ 816 120 67 32 46 24.5143%
Pair KK 814 122 67 32 46 24.6994%
Pair AA 818 118 67 32 46 24.3293%
Suited 34 815 114 66 40 46 24.6068%
Suited 35 816 113 66 40 46 24.5143%
Suited 45 817 112 66 40 46 24.4218%
Suited 36 816 113 66 40 46 24.5143%
Suited 46 817 112 66 40 46 24.4218%
Suited 56 818 111 66 40 46 24.3293%
Suited 37 817 112 66 40 46 24.4218%
Suited 47 818 111 66 40 46 24.3293%
Suited 57 819 110 66 40 46 24.2368%
Suited 67 819 110 66 40 46 24.2368%
Suited 38 818 111 66 40 46 24.3293%
Suited 48 818 111 66 40 46 24.3293%
Suited 58 819 110 66 40 46 24.2368%
Suited 68 819 110 66 40 46 24.2368%
Suited 78 820 109 66 40 46 24.1443%
Suited 39 818 111 66 40 46 24.3293%
Suited 49 819 110 66 40 46 24.2368%
Suited 59 819 110 66 40 46 24.2368%
Suited 69 819 110 66 40 46 24.2368%
Suited 79 820 109 66 40 46 24.1443%
Suited 89 820 109 66 40 46 24.1443%
Suited 3T 818 115 66 36 46 24.3293%
Suited 4T 819 114 66 36 46 24.2368%
Suited 5T 820 113 66 36 46 24.1443%
Suited 6T 819 114 66 36 46 24.2368%
Suited 7T 820 113 66 36 46 24.1443%
Suited 8T 820 113 66 36 46 24.1443%
Suited 9T 820 113 66 36 46 24.1443%
Suited 3J 817 116 66 36 46 24.4218%
Suited 4J 818 115 66 36 46 24.3293%
Suited 5J 819 114 66 36 46 24.2368%
Suited 6J 819 114 66 36 46 24.2368%
Suited 7J 819 114 66 36 46 24.2368%
Suited 8J 819 114 66 36 46 24.2368%
Suited 9J 819 114 66 36 46 24.2368%
Suited TJ 819 117 66 33 46 24.2368%
Suited 3Q 816 117 66 36 46 24.5143%
Suited 4Q 817 116 66 36 46 24.4218%
Suited 5Q 818 115 66 36 46 24.3293%
Suited 6Q 818 115 66 36 46 24.3293%
Suited 7Q 819 114 66 36 46 24.2368%
Suited 8Q 818 115 66 36 46 24.3293%
Suited 9Q 818 115 66 36 46 24.3293%
Suited TQ 818 118 66 33 46 24.3293%
Suited JQ 817 119 66 33 46 24.4218%
Suited 3K 815 118 66 36 46 24.6068%
Suited 4K 816 117 66 36 46 24.5143%
Suited 5K 817 116 66 36 46 24.4218%
Suited 6K 817 116 66 36 46 24.4218%
Suited 7K 818 115 66 36 46 24.3293%
Suited 8K 818 115 66 36 46 24.3293%
Suited 9K 817 116 66 36 46 24.4218%
Suited TK 817 119 66 33 46 24.4218%
Suited JK 816 120 66 33 46 24.5143%
Suited QK 815 121 66 33 46 24.6068%
Suited 3A 816 117 66 36 46 24.5143%
Suited 4A 817 116 66 36 46 24.4218%
Suited 5A 818 115 66 36 46 24.3293%
Suited 6A 819 114 66 36 46 24.2368%
Suited 7A 820 113 66 36 46 24.1443%
Suited 8A 820 113 66 36 46 24.1443%
Suited 9A 820 113 66 36 46 24.1443%
Suited TA 819 117 66 33 46 24.2368%
Suited JA 818 118 66 33 46 24.3293%
Suited QA 817 119 66 33 46 24.4218%
Suited KA 816 120 66 33 46 24.5143%
Unsuited 34 816 113 66 40 46 24.5143%
Unsuited 35 817 112 66 40 46 24.4218%
Unsuited 45 818 111 66 40 46 24.3293%
Unsuited 36 817 112 66 40 46 24.4218%
Unsuited 46 818 111 66 40 46 24.3293%
Unsuited 56 819 110 66 40 46 24.2368%
Unsuited 37 818 111 66 40 46 24.3293%
Unsuited 47 819 110 66 40 46 24.2368%
Unsuited 57 820 109 66 40 46 24.1443%
Unsuited 67 820 109 66 40 46 24.1443%
Unsuited 38 818 111 66 40 46 24.3293%
Unsuited 48 819 110 66 40 46 24.2368%
Unsuited 58 820 109 66 40 46 24.1443%
Unsuited 68 820 109 66 40 46 24.1443%
Unsuited 78 821 108 66 40 46 24.0518%
Unsuited 39 818 111 66 40 46 24.3293%
Unsuited 49 819 110 66 40 46 24.2368%
Unsuited 59 820 109 66 40 46 24.1443%
Unsuited 69 820 109 66 40 46 24.1443%
Unsuited 79 821 108 66 40 46 24.0518%
Unsuited 89 821 108 66 40 46 24.0518%
Unsuited 3T 818 115 66 36 46 24.3293%
Unsuited 4T 819 114 66 36 46 24.2368%
Unsuited 5T 820 113 66 36 46 24.1443%
Unsuited 6T 820 113 66 36 46 24.1443%
Unsuited 7T 821 112 66 36 46 24.0518%
Unsuited 8T 821 112 66 36 46 24.0518%
Unsuited 9T 821 112 66 36 46 24.0518%
Unsuited 3J 817 116 66 36 46 24.4218%
Unsuited 4J 818 115 66 36 46 24.3293%
Unsuited 5J 819 114 66 36 46 24.2368%
Unsuited 6J 819 114 66 36 46 24.2368%
Unsuited 7J 820 113 66 36 46 24.1443%
Unsuited 8J 820 113 66 36 46 24.1443%
Unsuited 9J 820 113 66 36 46 24.1443%
Unsuited TJ 820 117 66 32 46 24.1443%
Unsuited 3Q 816 117 66 36 46 24.5143%
Unsuited 4Q 817 116 66 36 46 24.4218%
Unsuited 5Q 818 115 66 36 46 24.3293%
Unsuited 6Q 818 115 66 36 46 24.3293%
Unsuited 7Q 819 114 66 36 46 24.2368%
Unsuited 8Q 819 114 66 36 46 24.2368%
Unsuited 9Q 819 114 66 36 46 24.2368%
Unsuited TQ 819 118 66 32 46 24.2368%
Unsuited JQ 818 119 66 32 46 24.3293%
Unsuited 3K 815 118 66 36 46 24.6068%
Unsuited 4K 816 117 66 36 46 24.5143%
Unsuited 5K 817 116 66 36 46 24.4218%
Unsuited 6K 817 116 66 36 46 24.4218%
Unsuited 7K 818 115 66 36 46 24.3293%
Unsuited 8K 818 115 66 36 46 24.3293%
Unsuited 9K 818 115 66 36 46 24.3293%
Unsuited TK 818 119 66 32 46 24.3293%
Unsuited JK 817 120 66 32 46 24.4218%
Unsuited QK 816 121 66 32 46 24.5143%
Unsuited 3A 817 116 66 36 46 24.4218%
Unsuited 4A 818 115 66 36 46 24.3293%
Unsuited 5A 819 114 66 36 46 24.2368%
Unsuited 6A 819 114 66 36 46 24.2368%
Unsuited 7A 820 113 66 36 46 24.1443%
Unsuited 8A 820 113 66 36 46 24.1443%
Unsuited 9A 820 113 66 36 46 24.1443%
Unsuited TA 820 117 66 32 46 24.1443%
Unsuited JA 819 118 66 32 46 24.2368%
Unsuited QA 818 119 66 32 46 24.3293%
Unsuited KA 817 120 66 32 46 24.4218%
billryan
billryan
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December 26th, 2016 at 9:17:34 AM permalink
Thank you, but I guess my question is more complicated than I thought.
Allow me to rephrase it.
Assume a player uses proper strategy and doesn't break up either a royal flush or five of a kind. That eliminates a number of the possibilities listed.
Drawing on three dueces, what are the chances of improving it beyond four of a kind?
Still in the 20-25 percent range? An exact percentage isn't necessary.
The older I get, the better I recall things that never happened
BobDancer
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December 26th, 2016 at 9:22:38 AM permalink
Quote: JB

It depends on the discards. For example, tossing unsuited Ace-Ten can make fewer Wild Royals than tossing 3-8.



Excellent response!

This website along with inquisitive gamblers everywhere are very fortunate that you are able and willing to calculate and publish stuff like this.

Thank you!
RS
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December 26th, 2016 at 9:22:40 AM permalink
Assuming JB's stuff is accurate, it's about 24-25%.
JB
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December 26th, 2016 at 9:41:41 AM permalink
Quote: billryan

Assume a player uses proper strategy and doesn't break up either a royal flush or five of a kind. That eliminates a number of the possibilities listed.
Drawing on three dueces, what are the chances of improving it beyond four of a kind?
Still in the 20-25 percent range?


Yes, just skip the hands that don't apply.
Including them, the range was 24.05% to 24.7%.
Excluding them, the range is 24.05% to 24.6%.
So a little worse than 1 in 4.
tringlomane
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December 26th, 2016 at 8:54:18 PM permalink
Quote: RS

Assuming JB's stuff is accurate, it's about 24-25%.



I can't recall the last time JB was wrong. Lol
Hunterhill
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December 26th, 2016 at 11:41:43 PM permalink
Quote: RS

Assuming JB's stuff is accurate, it's about 24-25%.

That's like saying, assuming JG's stuff is accurate-:)
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miplet
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December 27th, 2016 at 7:02:12 AM permalink
Quote: tringlomane

I can't recall the last time JB was wrong. Lol

My very first post here was from a JB error.
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billryan
billryan
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December 27th, 2016 at 8:48:43 AM permalink
I'd imagine one mistake every seven years or so is fairly acceptable. Unless we are talking marriages.
The older I get, the better I recall things that never happened
JB
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December 27th, 2016 at 12:01:07 PM permalink
I've made plenty of mistakes. Usually the quicker I respond to something, the more likely it is to be in error.

The figures in my table on page 1 came from WinPoker, which is known to contain an obscure bug, but I think it was accurate here.
RS
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December 27th, 2016 at 12:45:00 PM permalink
Quote: Hunterhill

That's like saying, assuming JG's stuff is accurate-:)



JB == JG


Coincidence?


You decide!
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