SOOPOO
SOOPOO
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March 3rd, 2019 at 6:08:24 AM permalink
I was playing pai gow poker at my local casino (Seneca Niagara) last night, probably a total of two hours, say 1.5 hand per deal on average, and hit two separate perfect lows. (2,3,4,5,7,8,9). Slowish players and slowish dealers, so probably only, say, 100 hands.

Help friends. What are the odds of getting the perfect low on any one hand, and then what are the odds of getting exactly two of them in 100 hands?

They were both "news" at the table, because just across the border there is a side bet that pays a lot (200-1?) for getting the perfect low, called pai gow insurance. No one at our table knew the actual payout for this lovely hand.....
Wizard
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kgb92
March 3rd, 2019 at 7:22:48 AM permalink
According to my page on pai gow poker side bets, the probability of a 9-high hand is 31080/154143080. Thank you for giving us the 100 hand assumption. For some reason, people seldom provide such information with questions like this. Using the binomial formula, the probability of exactly two 9-high hands out of 100 is 1 in 5068.311435.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
SOOPOO
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March 3rd, 2019 at 8:03:18 AM permalink
Quote: Wizard

According to my page on pai gow poker side bets, the probability of a 9-high hand is 31080/154143080. Thank you for giving us the 100 hand assumption. For some reason, people seldom provide such information with questions like this. Using the binomial formula, the probability of exactly two 9-high hands out of 100 is 1 in 5068.311435.



There are two possible 9 high pai gows. 2,3,4,5,7,8,9 and 2,3,4,6,7,8,9. I'll call the first one, the one I got both times, the BAD 9 high pai gow, and the second one, the GOOD one. Since each will happen equally, I'll assume the chances are 1/2 x 1/2 as likely as your calculations, so I experienced a 1 in 20,273 event. My perception through my years of playing would have been that it would be much rarer. I distinctly remember only two other perfect lows in my career. I'm up to four now.....

And thanks for doing the math...
GWAE
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March 3rd, 2019 at 8:16:19 AM permalink
I have a Stupid person math question. When someone says what are the odds of getting this when I played 100 hands. Does it matter if you get 1 then say what are the odds of getting another one in the next 99 hands . Opposed to sitting down and saying what are the odds of getting 2 in the next 100 hands.

This always confuses me because people will say I got 2 royals within 100 hands of each other and they think it is rare but they played 50k hands before the first and 50k after the second so really they are behind.
Last edited by: GWAE on Mar 3, 2019
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SOOPOO
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March 3rd, 2019 at 8:29:48 AM permalink
Quote: GWAE

Stupid person math question. When someone says what are the odds of getting this when I played 100 hands. Does it matter if you get 1 then say what are the odds of getting another one in the next 99 hands . Opposed to sitting down and saying what are the odds of getting 2 in the next 100 hands.

This always confuses me because people will say I got 2 royals within 100 hands of each other and they think it is rare but they played 50k hands before the first and 50k after the second so really they are behind.



If you analyze my question the answer is the answer to "what are the odds of getting 2 in the next 100 hands".
GWAE
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March 3rd, 2019 at 9:46:32 AM permalink
Quote: SOOPOO

If you analyze my question the answer is the answer to "what are the odds of getting 2 in the next 100 hands".



Sorry the stupid person wasnt meant towards your questions. I meant I am stupid when it comes to math and have a questiob
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SOOPOO
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March 3rd, 2019 at 10:15:07 AM permalink
Quote: GWAE

Sorry the stupid person wasnt meant towards your questions. I meant I am stupid when it comes to math and have a questiob



I didn't take it any other way! I thought I just clarified it for you!
Deucekies
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March 3rd, 2019 at 1:05:16 PM permalink
I wonder if the person who wrote "BEechwood 4-5789" played Pai Gow. ;)
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
sodawater
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March 3rd, 2019 at 2:53:35 PM permalink
Last year, I got a 9-high on the EZ pai gow table, which was full of Chinese betting the pai gow insurance side bet. When my hand was turned over and I was the only one who hadn't bet on the insurance, you should have heard the conversation.

By the way, I should mention that I can't stand EZ pai gow and its lack of banking, but it was the only open table and I was waiting for someone.
gamerfreak
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March 3rd, 2019 at 3:18:42 PM permalink
Quote: SOOPOO

Slowish players and slowish dealers, so probably only, say, 100 hands.


Not saying it couldn’t happen, but I think 50 HPH would be very fast if the table was full.

I think casinos rate for around 25-30 HPH with every spot filled.
GWAE
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March 3rd, 2019 at 4:02:46 PM permalink
Quote: SOOPOO

I didn't take it any other way! I thought I just clarified it for you!



Ok good. I guess I was just hijacking your thread a little since you got your answer. I was wondering if the odds were the same in both situations
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GWAE
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March 3rd, 2019 at 4:04:14 PM permalink
Quote: sodawater

Last year, I got a 9-high on the EZ pai gow table, which was full of Chinese betting the pai gow insurance side bet. When my hand was turned over and I was the only one who hadn't bet on the insurance, you should have heard the conversation.

By the way, I should mention that I can't stand EZ pai gow and its lack of banking, but it was the only open table and I was waiting for someone.



In Chinese I suspect? Did you know what they were saying. I wish I had the ability to learn a language. I would love to hear what is being said sometimes.
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SOOPOO
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March 3rd, 2019 at 4:35:42 PM permalink
Quote: gamerfreak

Not saying it couldn’t happen, but I think 50 HPH would be very fast if the table was full.

I think casinos rate for around 25-30 HPH with every spot filled.



I was playing two spots probably 60-70% of the time. And yes, 100 is really a guess.
unJon
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March 3rd, 2019 at 5:09:03 PM permalink
Quote: GWAE

I have a Stupid person math question. When someone says what are the odds of getting this when I played 100 hands. Does it matter if you get 1 then say what are the odds of getting another one in the next 99 hands . Opposed to sitting down and saying what are the odds of getting 2 in the next 100 hands.

This always confuses me because people will say I got 2 royals within 100 hands of each other and they think it is rare but they played 50k hands before the first and 50k after the second so really they are behind.



Those are very different questions. Much harder to get two in a hundred than 1 in 99.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
gamerfreak
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March 3rd, 2019 at 7:42:21 PM permalink
Quote: sodawater

By the way, I should mention that I can't stand EZ pai gow and its lack of banking, but it was the only open table and I was waiting for someone.


RIP Dan but I also dislike EZ Paigow. Rooting for the dealer to draw a Queen High paigow when you have a mediocre hand is a really fun component of standard PGP. IMO that rule change is not worth eliminating the comission.
PlayYourCardsRight
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March 3rd, 2019 at 10:23:35 PM permalink
I love EZ pai gow. Game goes quicker because dealers aren't f!#/ing up the commissions. The Q high side bet adds a little something to the game. Waiting to lay face up, which hasn't reached my corner of the world yet.

(Warning. No f-bombs! KEEP it PG.)
Last edited by: beachbumbabs on Mar 4, 2019
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