ChurchVanCrash
ChurchVanCrash
Joined: Jul 18, 2017
  • Threads: 1
  • Posts: 6
April 1st, 2021 at 2:19:32 PM permalink
When holding 4 suited cards, is hitting a flush 1 out of 29 times within the standard deviations for video poker?
unJon
unJon
Joined: Jul 1, 2018
  • Threads: 14
  • Posts: 2372
April 1st, 2021 at 2:31:40 PM permalink
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?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
teliot
teliot
Joined: Oct 19, 2009
  • Threads: 39
  • Posts: 2159
Thanks for this post from:
WTflush
April 1st, 2021 at 2:45:23 PM permalink
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.
Personal website: www.ijmp.org
SOOPOO
SOOPOO
Joined: Aug 8, 2010
  • Threads: 109
  • Posts: 7711
April 1st, 2021 at 2:52:34 PM permalink
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.
ChurchVanCrash
ChurchVanCrash
Joined: Jul 18, 2017
  • Threads: 1
  • Posts: 6
April 1st, 2021 at 3:36:53 PM permalink
Okay, but are you saying itís outside of the standard deviations for video poker?
charliepatrick
charliepatrick
Joined: Jun 17, 2011
  • Threads: 33
  • Posts: 2324
Thanks for this post from:
teliot
April 1st, 2021 at 3:54:35 PM permalink
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!).
teliot
teliot
Joined: Oct 19, 2009
  • Threads: 39
  • Posts: 2159
April 1st, 2021 at 5:07:41 PM permalink
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.
Personal website: www.ijmp.org
teliot
teliot
Joined: Oct 19, 2009
  • Threads: 39
  • Posts: 2159
April 1st, 2021 at 5:09:20 PM permalink
Quote: ChurchVanCrash

Okay, but are you saying itís 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)!
Last edited by: teliot on Apr 1, 2021
Personal website: www.ijmp.org
ChurchVanCrash
ChurchVanCrash
Joined: Jul 18, 2017
  • Threads: 1
  • Posts: 6
April 3rd, 2021 at 4:03:13 PM permalink
The 29 draws comes from noting over time that 4 cards to a flush draws donít ever seem to hit and then keeping track of it. Not from cherry picking results.
billryan
billryan
Joined: Nov 2, 2009
  • Threads: 178
  • Posts: 10275
April 3rd, 2021 at 4:13:22 PM permalink
Quote: ChurchVanCrash

The 29 draws comes from noting over time that 4 cards to a flush draws donít 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.

  • Jump to: