TOPDOG
Joined: Mar 18, 2023
• Posts: 4
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March 18th, 2023 at 8:16:20 AM permalink
I've searched a few sites and maybe I'm just an idiot but can't seem to find a site that can answer my question. I know what the odds are for hitting a straight flush with 52 cards but what I'm curious about is what are the odds of hitting a straight flush with only using the 2s,3s,4s,5s,6s,7s,8s and 9s??? If someone could assist me that would be great and IF you can could you also assist me in letting me know the calculations needs to determine the odds??
Thank you
Mission146
Joined: May 15, 2012
• Posts: 16204
March 18th, 2023 at 8:22:00 AM permalink
Does the deck only use 2-9 or are you saying you want the highest SF to be 5-6-7-8-9 in a regular deck?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
TOPDOG
Joined: Mar 18, 2023
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March 18th, 2023 at 8:38:52 AM permalink
I guess you could say the deck is only using the 2s through 9s. No Ts, Js, Qs, Ks, or As. So only using 32 cards total as oppossed to the traditional full deck of 52 cards
TOPDOG
Joined: Mar 18, 2023
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March 18th, 2023 at 8:41:30 AM permalink
Futher - the payout will happen if any straight flush happens. Could be 2,3,4,5,6 or 3,4,5,6,7 or 4,5,6,7,8 or 5,6,7,8,9. Not just the straight but has to be the straight flush
Mission146
Joined: May 15, 2012
• Posts: 16204
March 18th, 2023 at 8:47:43 AM permalink
Quote: TOPDOG

Futher - the payout will happen if any straight flush happens. Could be 2,3,4,5,6 or 3,4,5,6,7 or 4,5,6,7,8 or 5,6,7,8,9. Not just the straight but has to be the straight flush

Right. The first thing to do is figure out how many straight flushes there are:

2-3-4-5-6 (1)
3-4-5-6-7 (2)
4-5-6-7-8 (3)
5-6-7-8-9 (4)

4 * 4 = 16

The next thing we have to do is figure out how many total cards there are:

2 3 4 5 6 7 8 9 ---> 8 * 4 = 32

The next thing we have to do is figure out how many ways we can pick five of 32 cards:

https://web2.0calc.com/

nCr(32,5) = 201,376

The next thing we have to do is divide the number of combinations that give us a straight flush by the total possible number of combinations:

16/201376 = 0.0000794533608772 or 0.00794533608772%--->1 in 12,586 to be dealt a straight flush.

Significantly more likely than with a full deck.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
TOPDOG
Joined: Mar 18, 2023
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March 18th, 2023 at 9:18:21 AM permalink
Thank you so much. That was very helpful. So now I'll throw in a monkey wrench and ask how to calculate the odds if there are 2 Jokers (wild cards) thrown into the mix and off the 34 TOTAL cards in play only 20 cards are drawn to show 4 different 5 card hands
Mission146
Joined: May 15, 2012
• Posts: 16204
March 18th, 2023 at 10:02:14 AM permalink
Quote: TOPDOG

Thank you so much. That was very helpful. So now I'll throw in a monkey wrench and ask how to calculate the odds if there are 2 Jokers (wild cards) thrown into the mix and off the 34 TOTAL cards in play only 20 cards are drawn to show 4 different 5 card hands

Perhaps one of the guys good at programming will be along for this one. I could do it, but it would take me longer than I want to spend. Sorry about that.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5675
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March 18th, 2023 at 10:08:33 AM permalink
Quote: TOPDOG

Thank you so much. That was very helpful. So now I'll throw in a monkey wrench and ask how to calculate the odds if there are 2 Jokers (wild cards) thrown into the mix and off the 34 TOTAL cards in play only 20 cards are drawn to show 4 different 5 card hands

Do you want to know the probability that a 5-card hand will be a straight flush, or that, if you are dealt four separate hands from the 34-card deck, that at least one of them is a straight flush? The second one is a harder problem.

For the first one, first determine how many ways there are of getting a straight flush:
No jokers: 23456, 34567, 45678, 56789
One joker: for each of the "no jokers" sets, there are 5 ways to replace a card with a joker - but that counts three sets twice (J3456 and 3456J; J4567 and 4567J; J5678 and 5678J), so that's 17 ways
Two jokers is slightly harder - for now, just count them:
From 23456: 234, 235, 236, 245, 246, 256, 345, 346, 356, 456
From 34567: since every set of 3 numbers in 3456 was already counted in 23456, count just the ones with a 7 in them: 347, 357, 367, 457, 467, 567
From 45678: since every set of 3 numbers in 4567 has already been counted, count just the ones with an 8 in them: 458, 468, 478, 568, 578, 678
From 56789: since every set of 3 numbers in 5678 has already been counted, count just the ones with an 9 in them: 569, 579, 589, 679, 689, 789
That is a total of 28
Since each straight flush can be one of four suits, the total is 4 * (4 + 17 + 28) = 196
There are C(34,5) = 278,256 hands, so the probability is 196 / 278,256, or about 1 / 9938
Mission146
Joined: May 15, 2012
• Posts: 16204
March 18th, 2023 at 10:30:36 AM permalink
Quote: ThatDonGuy

Quote: TOPDOG

Thank you so much. That was very helpful. So now I'll throw in a monkey wrench and ask how to calculate the odds if there are 2 Jokers (wild cards) thrown into the mix and off the 34 TOTAL cards in play only 20 cards are drawn to show 4 different 5 card hands

Do you want to know the probability that a 5-card hand will be a straight flush, or that, if you are dealt four separate hands from the 34-card deck, that at least one of them is a straight flush? The second one is a harder problem.

For the first one, first determine how many ways there are of getting a straight flush:
No jokers: 23456, 34567, 45678, 56789
One joker: for each of the "no jokers" sets, there are 5 ways to replace a card with a joker - but that counts three sets twice (J3456 and 3456J; J4567 and 4567J; J5678 and 5678J), so that's 17 ways
Two jokers is slightly harder - for now, just count them:
From 23456: 234, 235, 236, 245, 246, 256, 345, 346, 356, 456
From 34567: since every set of 3 numbers in 3456 was already counted in 23456, count just the ones with a 7 in them: 347, 357, 367, 457, 467, 567
From 45678: since every set of 3 numbers in 4567 has already been counted, count just the ones with an 8 in them: 458, 468, 478, 568, 578, 678
From 56789: since every set of 3 numbers in 5678 has already been counted, count just the ones with an 9 in them: 569, 579, 589, 679, 689, 789
That is a total of 28
Since each straight flush can be one of four suits, the total is 4 * (4 + 17 + 28) = 196
There are C(34,5) = 278,256 hands, so the probability is 196 / 278,256, or about 1 / 9938