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What is the probability of a dealer winning 5,6 or 7 hands in a row in Pai Gow Poker (omit pushes)

June 14th, 2012 at 11:08:38 AM permalink
paigowsteve
Member since: Jun 14, 2012
Threads: 1
Posts: 3
Just wondering what the percentage chance of the Pai Gow dealer winning 5,6 or 7 hands in a row, disregarding ties,pushes, since no money changes hands.
June 14th, 2012 at 11:44:27 AM permalink
buzzpaff
Member since: Mar 8, 2011
Threads: 112
Posts: 5328
7 hands is 127.345627 approximately.
June 14th, 2012 at 11:57:57 AM permalink
rdw4potus
Member since: Mar 11, 2010
Threads: 78
Posts: 5635
Quote: buzzpaff
7 hands is 127.345627 approximately.


I'm glad you rounded that off:-)

the dealer wins a little over 50% of the time, depending on the exact set of hand-setting rules that the player and dealer are using. so .5ish^n is the formula to use to find the probability of the dealer winning n hands in a row. taking 1/result will give the to-1 version of the answer (like Buzz's 1:127 above)
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June 14th, 2012 at 1:09:30 PM permalink
98Clubs
Member since: Jun 3, 2010
Threads: 38
Posts: 1313
I actually got 1 in 109.75 using 28.61% as Player and 29.91% as Dealer figuring 7 straight Dealer wins no push. This from WoO site.
Nonetheless, rather common. For 7 straight hands dealt the odds are about 1 in 4670 that the Dealer will win all 7.
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June 14th, 2012 at 3:56:41 PM permalink
paigowsteve
Member since: Jun 14, 2012
Threads: 1
Posts: 3
THANKS, seems a little stronger than I thought, but Thanks for the quick answer.
June 14th, 2012 at 4:20:12 PM permalink
RaleighCraps
Member since: Feb 20, 2010
Threads: 62
Posts: 1826
Well, if RaleighCraps is at the table the odds of the dealer winning 100 in a row is about 1:1.

Man I hate the way that game treats me...................
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June 14th, 2012 at 5:47:43 PM permalink
mustangsally
Member since: Mar 29, 2011
Threads: 7
Posts: 563
Quote: paigowsteve
THANKS, seems a little stronger than I thought, but Thanks for the quick answer.
The answers given so far are for exactly the very next 7 non-tie hands.

I also get a 51.11% win probability for the Dealer.

.91% or
1 in 109.8 for the very next 7 hands

The average number of hands looks to be about 223 to see 7 in a row.

What would the probability be in the next 50 hands?
And there could even be 2 such streaks?
18.7%
about 18 times more likely

How about 100 hands?
35.4% for at least 1 such streak of 7 wins in a row (over 350,000 out of 1 million players would see such a streak in 100 hands)
6.2% for at least 2 such streaks of 7 wins in a row (about 1 in 16)

How about 1000 hands?
One can expect to see, on average, about 4.4 such streaks
and about a 1 in 6 chance of seeing at least 7 such streaks of 7 winners in a row by the Dealer.


Streak Calculator
Includes Links to spreadsheets and the math to do this yourself if interested.
Sally
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June 14th, 2012 at 8:29:47 PM permalink
paigowsteve
Member since: Jun 14, 2012
Threads: 1
Posts: 3
THANKS for the link to the Streak Calculator, Mustangsally

 

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