Four cards to a Flush Draw
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April 1st, 2021 at 2:19:32 PM
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When holding 4 suited cards, is hitting a flush 1 out of 29 times within the standard deviations for video poker?
April 1st, 2021 at 2:31:40 PM
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Over how many observations of holding four cards?Quote: ChurchVanCrashWhen holding 4 suited cards, is hitting a flush 1 out of 29 times within the standard deviations for video poker?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
April 1st, 2021 at 2:45:23 PM
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This was my first thought as well, cherry picking the trials.Quote: unJonOver how many observations of holding four cards?
But, to answer the question.
p = p(Flush) = 9/47.
The standard deviation is 2.118918214
The expected value is 5.553191489
So getting 1 out of 29 is 2.148828 standard deviations below expectation.
p(0 Flushes in 29 trials) = (1-9/47)^29 = 0.002103228
P(1 Flushes in 29 trials) = 29*(1-9/47)^28*(9/47) = 0.014445858 (about 1-in-69).
P(0 or 1 Flushes in 29 trials) = 0.016549086 (about 1-in-60).
I'd call this a Tuesday.
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April 1st, 2021 at 2:52:34 PM
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Quote: unJonOver how many observations of holding four cards?
If you take the OP literally, he had 4 suited cards 29 times and only hit a flush 1 of those 29 times. Expected around 6. 1 certainly more than a Standard Deviation from expected.
April 1st, 2021 at 3:36:53 PM
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Okay, but are you saying it’s outside of the standard deviations for video poker?
April 1st, 2021 at 3:54:35 PM
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I agree with Eliot's figures (using Av=np and SD=SQRT(npq) n=29 p=9/47 q=38/47). What that shows it's just above 2SDs.
If you played fairly often and on one particular day had some bad luck with your flush draws, then it would be perfectly reasonable to see this - i.e. if you bet long enough you will have good days and bad days.
if you were testing out a casino for fairness and stated up front you were looking at how often it let you hit your hands then you would probably put this down to bad luck rather than anything suspicious. However if it happened to other types of hands (e.g. missing making outside straights etc) then you would have reasonable grounds to be suspicious and make further tests.
As Eliot says - it must be Tuesday (even though it's actually Thursday here!).
If you played fairly often and on one particular day had some bad luck with your flush draws, then it would be perfectly reasonable to see this - i.e. if you bet long enough you will have good days and bad days.
if you were testing out a casino for fairness and stated up front you were looking at how often it let you hit your hands then you would probably put this down to bad luck rather than anything suspicious. However if it happened to other types of hands (e.g. missing making outside straights etc) then you would have reasonable grounds to be suspicious and make further tests.
As Eliot says - it must be Tuesday (even though it's actually Thursday here!).
April 1st, 2021 at 5:07:41 PM
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We can also assume there was another flush on the trial either before the 29 or after (or both), since 29 is such an "odd" number. I'd say perfectly reasonable outcome.Quote: SOOPOOIf you take the OP literally, he had 4 suited cards 29 times and only hit a flush 1 of those 29 times. Expected around 6. 1 certainly more than a Standard Deviation from expected.
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April 1st, 2021 at 5:09:20 PM
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This language doesn't make sense. The outcome is more than 1 standard deviation from the mean, but it is less than 2.12 standard deviations from the mean.Quote: ChurchVanCrashOkay, but are you saying it’s outside of the standard deviations for video poker?
If you don't know what you are asking, how will you know if we answered it?
But what is almost certainly the case is that there were 3 flushes in 31 attempts and you selected out the endpoints to get 1 in 29. In the 3-in-31 case this is 1.34 standard deviations below expectation, or a 1-in-7.7 shot. That really is a Tuesday (or a Thursday, as I was correctly corrected)!
Last edited by: teliot on Apr 1, 2021
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April 3rd, 2021 at 4:03:13 PM
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The 29 draws comes from noting over time that 4 cards to a flush draws don’t ever seem to hit and then keeping track of it. Not from cherry picking results.
April 3rd, 2021 at 4:13:22 PM
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Quote: ChurchVanCrashThe 29 draws comes from noting over time that 4 cards to a flush draws don’t ever seem to hit and then keeping track of it. Not from cherry picking results.
If you play VP long enough, you'll see some very unusual streaks.
The older I get, the better I recall things that never happened
April 3rd, 2021 at 5:10:34 PM
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I'm glad this topic came up. I have the worst results trying hit flushes with four cards held. If I didnt know better I'd say the machines were rigged.
I'm glad I'm not alone.
I'm glad I'm not alone.
April 3rd, 2021 at 6:21:44 PM
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Now it’s 1 out of 32.
April 3rd, 2021 at 6:29:49 PM
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1 out of 34.
April 7th, 2021 at 1:31:35 PM
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4 out of 48
April 7th, 2021 at 5:21:46 PM
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Quote: ChurchVanCrash4 out of 48
Your most recent results are 3/14
The older I get, the better I recall things that never happened
April 7th, 2021 at 5:52:04 PM
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Quote: AlanMendelsonI'm glad this topic came up. I have the worst results trying hit flushes with four cards held. If I didnt know better I'd say the machines were rigged.
I'm glad I'm not alone.
can i quote you on this. lol jk i just did
April 20th, 2021 at 10:18:25 AM
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4 out of 57
April 21st, 2021 at 4:02:03 PM
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Played Jacks or Better at a California tribal casino last night and made a flush 1 out of 14 times when holding 4 suited cards. Could there be someone somewhere who thought that .0714 looked like a better number than .1875 did?
