100xOdds
100xOdds
Joined: Feb 5, 2012
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June 3rd, 2019 at 9:10:17 AM permalink


not only did I get quad Queens by holding only 1 card but I also hit all three 4x multipliers.
so 3 quads at 4x. :)

I think there's only 1 way to get the other Queens such that I use all three 4x multipliers.
and that is they all have to be in the same row as the multipliers.

i think Lady Luck REALLY smiled on me.
What are the odds of this happening?
Last edited by: 100xOdds on Jun 3, 2019
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
DogHand
DogHand
Joined: Sep 24, 2011
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June 3rd, 2019 at 10:17:29 AM permalink
Quote: 100xOdds



not only did I get quad Queens by holding only 1 card but I also hit all three 4x multipliers.
so 3 quads at 4x. :)

I think there's only 1 way to get the other Queens such that I use all three 4x multipliers.
and that is they all have to be in the same row as the multipliers.

i think Lady Luck REALLY smiled on me.
What are the odds of this happening?



100xOdds,

Well, assuming the four cards you discarded are all singletons (say, a 2, a 5, a 7, and a 9), you can hold one card and get quads two ways: draw the three cards that match the one held plus a fourth random card, or draw quads (for example, hold a club Q and draw 4 6's).

The first possibility is given by this: from the remaining 47 cards you have to draw the QS, the QH, the QD, and any other card, but since the order doesn't matter, you have to account for the fact that you can draw these 4 cards in 4! = 4*3*2*1 = 24 ways:

Quad Q's probability = 24*(1/47)*(1/46)*(1/45)*(44/44) = 0.0002466851...

The second possibility (for any possible set of quads other than Q's) is given by this: from the remaining 47 cards, draw one that is NOT one of the three remaining Q's, 2's, 5's, 7's, or 9's; then draw its three matches, once again accounting for the 24 equivalent orders:

Other quad probability = 24*(32/47)*(1/46)*(1/45)*(1/44) = 0.0001794073...

Adding these together gives:

Quad probability = 0.0004260925...

or about 1 in 2347.

Hope this helps!

Dog Hand
100xOdds
100xOdds
Joined: Feb 5, 2012
  • Threads: 516
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June 3rd, 2019 at 10:31:12 AM permalink
Quote: DogHand

Adding these together gives:
Quad probability = 0.0004260925...
or about 1 in 2347.

Hope this helps!

Dog Hand


thx!
in spin poker you are playing 9 lines.
to use all three 4x multipliers in my OP, that quad had to be in exactly 1 place.

what are the odds of getting quads on a specific line while holding 1 card?
2347 x 9 (since there are 9 lines) = 1 in 21k?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)

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