Four cards to a Flush Draw

When holding 4 suited cards, is hitting a flush 1 out of 29 times within the standard deviations for video poker?

Quote: ChurchVanCrash

When holding 4 suited cards, is hitting a flush 1 out of 29 times within the standard deviations for video poker?

Over how many observations of holding four cards?

Quote: unJon

Over how many observations of holding four cards?

This was my first thought as well, cherry picking the trials.

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.

Quote: unJon

Over 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.

Okay, but are you saying it’s outside of the standard deviations for video poker?

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!).

Quote: SOOPOO

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.

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: ChurchVanCrash

Okay, but are you saying it’s outside of the standard deviations for video poker?

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.

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)!

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.

Quote: ChurchVanCrash

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.

If you play VP long enough, you'll see some very unusual streaks.