Chances of a 7-card copy in Pai Gow Poker

Apologies if this has been asked before. I searched to no avail.

What are the chances of the dealer and the player having a seven-card copy? Identical 5-card hand and identical two-card hand?

I figure that if we're talking about two Pai Gows, it would be something to the effect of (3/40)*(3/39)*(3/38)...etc, to the seventh power in order to disregard order. However, that doesn't account for pairs.

I'm sure somebody has done the math on it at some point. Any help would be greatly appreciated.

Quote: Deucekies

Apologies if this has been asked before. I searched to no avail.

What are the chances of the dealer and the player having a seven-card copy? Identical 5-card hand and identical two-card hand?

I figure that if we're talking about two Pai Gows, it would be something to the effect of (3/40)*(3/39)*(3/38)...etc, to the seventh power in order to disregard order. However, that doesn't account for pairs.

I'm sure somebody has done the math on it at some point. Any help would be greatly appreciated.

From the Pai Gow Poker - FAQ

Based on a simulation of 7.7 billion hands, assuming the player follows the house way, the probability of a copy in the front (low) hand is 2.55%, or 1 in 39.24. The probability of a copy in the back (high) hand is 0.038%, or 1 in 2,637. The probability of a double copy is about 1 in 78,200.

Eureka! Thank you very much!

Quote: Deucekies

Eureka! Thank you very much!

I had one this last trip to Vegas in January. My second one. This time was very painful, as I was banking every other hand. I wasn't the banker for the 7 card copy....
This one was a q high pai gow. Too bad I wasn't playing EZ pai gow.....

The discussion I was having with someone was how the odds of a 7-card copy compare to the odds of a 7-card natural straight flush. Someone said at one point that the 7-card copy was harder to do, and it grew legs. Obviously 78,000 is a lot less than 5,000,000.

I imagine some intrepid game inventor has already patented a side bet on dealer copies and is squatting on it.

Quote: SOOPOO

I had one this last trip to Vegas in January. My second one. This time was very painful, as I was banking every other hand. I wasn't the banker for the 7 card copy....
This one was a q high pai gow. Too bad I wasn't playing EZ pai gow.....

Where were you playing? Just curious. I haven't banked PGP in a while but may do some next time I'm in Vegas.

Quote: AcesAndEights

Where were you playing? Just curious. I haven't banked PGP in a while but may do some next time I'm in Vegas.

First one was at Seneca Niagara Casino in Niagara Falls, USA. This recent one was at the Rio.