One for the Mathematicians

[bigbear]

Ok,this will sound like the most unlikely story ever but I swear on my life that it is true.Just back off a cruise where the ship had an onboard casino which included a three card poker table.On the last night,i hit consecutive straight flushes which is a rarity in itself.However not only did they come in two hands,they came with the SAME cards (jack,queen,king of clubs).Would love to know the odds of that happening but it must be millions to one against.

 

[rockycatt]

BELIEVE THIS OR NOT I ONCE playing gin rummy in a coffee house got gin on the go as also did the house dealer at the same time same game

 

[mathsboy1975]

Ok,this will sound like the most unlikely story ever but I swear on my life that it is true.Just back off a cruise where the ship had an onboard casino which included a three card poker table.On the last night,i hit consecutive straight flushes which is a rarity in itself.However not only did they come in two hands,they came with the SAME cards (jack,queen,king of clubs).Would love to know the odds of that happening but it must be millions to one against.

If you look at it that you have a 3 card hand (any 3 cards) and you want to know the probability of getting those same cards dealt to you on the subsequent hand, then it is just equal to

(3/52) x (2/51) x (1/50) = 1/22100

which is just the probability of getting dealt any 3 specific cards (in any order). If you wanted to know the chances of getting those 3 cards dealt TWICE in a row it would be that value squared

= 1/488410000

For example you start a game and play 2 hands - that value is the probability that you get dealt JQK of clubs in both hands.

For ANY two successive 3 card straight flushes (not necessarily the SAME straight flush - just 2 consecutive straight flushes) it is a little more complicated. First of all the value of 1/22100 indicates the probability of getting dealt ANY specific hand so that tells you there are a total of 22100 possible distinct 3 card poker hands (ignoring the ORDER dealt in). From this total of 22100, there are 48 possible straight flushes - 12 for each suit according to

A23,234,345,456,567,678,789,910J,10JQ,JQK,QKA

Therefore the possibility of getting a straight flush on any hand is just

48/22100

which is roughly

0.00217

Now to get 2 straight flushes in a row, would mean that we must square this value which is roughly

0.00000472

which is roughly

1/211984

I am fairly sure that the above is correct but I have had a considerable amount to drink so feel free to shoot it down....

 

[dunover]

If you look at it that you have a 3 card hand (any 3 cards) and you want to know the probability of getting those same cards dealt to you on the subsequent hand, then it is just equal to

(3/52) x (2/51) x (1/50) = 1/22100

which is just the probability of getting dealt any 3 specific cards (in any order). If you wanted to know the chances of getting those 3 cards dealt TWICE in a row it would be that value squared = 1/488410000

For example you start a game and play 2 hands - that value is the probability that you get dealt JQK of clubs in both hands.

For ANY two successive 3 card straight flushes (not necessarily the SAME straight flush - just 2 consecutive straight flushes) it is a little more complicated. First of all the value of 1/22100 indicates the probability of getting dealt ANY specific hand so that tells you there are a total of 22100 possible distinct 3 card poker hands (ignoring the ORDER dealt in). From this total of 22100, there are 48 possible straight flushes - 12 for each suit according to

A23,234,345,456,567,678,789,910J,10JQ,JQK,QKA

Therefore the possibility of getting a straight flush on any hand is just

48/22100

which is roughly

0.00217

Now to get 2 straight flushes in a row, would mean that we must square this value which is roughly

0.00000472

which is roughly

1/211984

I am fairly sure that the above is correct but I have had a considerable amount to drink so feel free to shoot it down....

Can't fault the maths, but the logic is slightly out. The event was 1/22100, simple as. He got the same 3 twice consecutively. That those 3 were a SF is irrelevant. Basically a 1/1 x 1/22100 event.

If however he predicted those 3 cards in advance (which he didn't) the odds would indeed have been 22100^2

 

[mathsboy1975]

Can't fault the maths, but the logic is slightly out. The event was 1/22100, simple as. He got the same 3 twice consecutively. That those 3 were a SF is irrelevant. Basically a 1/1 x 1/22100 event.

If however he predicted those 3 cards in advance (which he didn't) the odds would indeed have been 221002

Yeah I lost what was being asked halfway through answering but I think I did mention that and then specified the square for any 2 specified hands in a row. Now rereading the original post, I guess that the answer he is looking for might actually be

(48/22100) x (1/22100)

as that is the odds of getting dealt ANY straight flush on the first hand, and then exactly the same one on the next hand.

That is roughly 1 in 10175208

 

[Simmo!]

Congrats to the 2 geeks ^ for working that one out but double congrats to the OP 'cos that's a special win in the only card game I play Hopefully you were playing Pair Plus but were you betting Prime too for a small kicker? I know it's a silly bet statistically but it adds to the fun.

 

[jjezebel37]

Need to get some of these guys on Countdown

 

[dunover]

Need to get some of these guys on Countdown

Yes, I'd like to have a few games with Rachel Riley......

 

[dunover]

Yeah I lost what was being asked halfway through answering but I think I did mention that and then specified the square for any 2 specified hands in a row. Now rereading the original post, I guess that the answer he is looking for might actually be

(48/22100) x (1/22100)

as that is the odds of getting dealt ANY straight flush on the first hand, and then exactly the same one on the next hand.

That is roughly 1 in 10175208

Yeah, I can go with that.

Utter spawn anyway! If he plays today and gets a 5-reel WD or Sh!tstorm then all the shiny stuff off of the Christmas tree will get wrapped around my head....

 

[bigbear]

Congrats to the 2 geeks ^ for working that one out but double congrats to the OP 'cos that's a special win in the only card game I play Hopefully you were playing Pair Plus but were you betting Prime too for a small kicker? I know it's a silly bet statistically but it adds to the fun.

Yes,i was playing the Pair Plus but on the ship they did not have the Prime option.Instead they had an optional side bet where you could combine five out of the six cards from your hand and the dealers hand to make anything from a straight upwards.It all looked a bit weird so I didn't bother and there were very few payouts.However a royal flush paid odds of 10000 to 1 but I was told that this had only ever happened twice.

 

[bigbear]

Thanks everyone for all the info and for taking the time to calculate all the figures