AZMango
AZMango
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June 8th, 2023 at 8:42:23 AM permalink
I was recently dealt a sequential straight flush. I haven't had any luck finding the odds of such a thing happening. I was able to find the odds of a dealt straight flush but not sequential. I don't know how to calculate it myself. Does anyone know?

Thanks
UP84
UP84
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June 8th, 2023 at 8:52:55 AM permalink
There are 311,875,200 possible ways to draw 5 cards - 52x51x50x49x48.
For each of the 4 suits there are 9 possible sequential straight flushes (excluding a royal flush).
So the odds of being dealt a sequential straight flush would be 36/311,875,200 or 1 in 8,663,200
Last edited by: UP84 on Jun 8, 2023
AZMango
AZMango
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June 8th, 2023 at 9:24:44 AM permalink
Thanks for the quick response. I assume this only includes one direction of straight flush. So, are the odds then 72/311,875,200 if reversible straight flushes are also included. Seems like they should be.

As an aside, does that mean that a dealt sequential royal flush is 4/311,875,200? Then 8/311,875,200 for the reverse royal? My dealt straight flush was 9 through King.

Thanks again.
UP84
UP84
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June 8th, 2023 at 9:26:16 AM permalink
Quote: AZMango

Thanks for the quick response. I assume this only includes one direction of straight flush. So, are the odds then 72/311,875,200 if reversible straight flushes are also included. Seems like they should be.

As an aside, does that mean that a dealt sequential royal flush is 4/311,875,200? Then 8/311,875,200 for the reverse royal? My dealt straight flush was 9 through King.

Thanks again.
link to original post

Correct. In my earlier answer, I assumed one-way sequential.
AZMango
AZMango
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June 8th, 2023 at 9:48:21 AM permalink
So, did I actually beat the one-way sequential odds since my straight flush wasn't reversed? I guess it depends on whether low to high or high to low is the default order. Either way, I should have gotten a picture since it's very unlikely I'll ever get another dealt sequential straight flush.
UP84
UP84
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June 8th, 2023 at 10:05:02 AM permalink
It all depends on how "sequential" is defined.

If "sequential" is defined to mean only low-to-high left-to-right, then your 9-K straight flush was a 1 in 8,663,200 event.
If "sequential" is defined to mean either low-to-high left-to-right or high-to-low left-to-right, then your 9-K straight flush was a 1 in 4,331,600 event.

Either way, you definitely should have taken a picture!!
AZMango
AZMango
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June 8th, 2023 at 10:17:30 AM permalink
Yep. I think I got side tracked because it was almost a royal and that it didn't pay any more than a regular four of a kind. My wife was watching and asked, "Does it pay more since it's in order?" It did pay a bit more since I was playing 100 line pennies. But, it would have been way more for the dealt royal. I realized I didn't take a picture as soon as I dealt the next hand. I did get a picture of a royal I got later on a dollar machine.
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