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 difference between fiction and reality is that fiction is supposed to make sense.
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 difference between fiction and reality is that fiction is supposed to make sense.
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 difference between fiction and reality is that fiction is supposed to make sense.
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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