bigfoot66
bigfoot66
Joined: Feb 5, 2010
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May 11th, 2021 at 11:07:03 PM permalink
Q: What are the odds of being dealt three to a royal in video poker?
I assume it is (47C2 × 5C3)/(52C5) = 1/60 but on vp sites i keep seeing the odds as 1 in 92.
I think I am right, just that the 1 in 92 is excluding hands like TJQAA where you hold AA > TJQs, any of the people on here better at math than me (a weak criteria, indeed) care to share their opinion on this?
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sabre
sabre
Joined: Aug 16, 2010
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May 12th, 2021 at 4:34:36 AM permalink
Your math looks right. You did omit multiplying by 4 to account for suits but your 1/60 calculation factors that in.

The 1 in 92 figure probably does account for high pairs, pat straights and pat flushes containing 3 to a royal.
drrock
drrock
Joined: Mar 6, 2012
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May 12th, 2021 at 10:05:31 AM permalink
Yep, I would agree with sabre that there are different odds of being dealt a 3-card royal draw vs. actually choosing to hold those 3 cards.

To sabre's list, you might want to add in hands with trips, 4-card straight flush draws, and hands containing 2 Pair, along with the occasional 4-card flush draw when its EV exceeds the 3-card royal flush draw. Deuces or Joker Wild games will cause the above list to vary.

Given that, you would see that the 1 in 92 figure changes from game to game and is also dependent to a small degree on whether you are playing a strategy that accounts for penalty cards.
bigfoot66
bigfoot66
Joined: Feb 5, 2010
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May 12th, 2021 at 10:58:39 AM permalink
Thanks, that's what I thought was going on but couldn't ignore the possibility that I was making an error.
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