Table Games Yet another math (odds) question...

In Pai Gow Poker on the fortune bonus bet pays 50:1 for a straight flush. What are the odds of 2 separate trips in a 2 month time frame each producing 1 straight flush win.

This actually happened to me and I feel like I'm on cloud 9! In AC last month and in Harrah's Philadelphia yesterday. Maybe I should go buy a lottery ticket!

 

According to the "Wizard of Odds" ... the probability of getting a straight flush (not including a Royal) is approx. 1 out of 455.

Getting a 2nd one, a month later, at a completely different property, would be totally independent of your first one. Still the same probability.

 

Right....events are independent.

However, the OP wasn't asking, from the perspective of the day before the 2nd hit, what his odds were of hitting again. Nor, is he asking what the odds are of him hitting again today.

The OP is asking, from the perspective of the day before the 1st hit, what the odds were of hitting twice on two separate trips in a 2 month period. And the answer to that is dependent on how many pai gow hands he played for each trip.

After all, let's imagine that on the first trip, he played 10,000 hands, and on the second trip, he played another 10,000 hands. The odds of hitting the straight flush at least once on each trip is extremely high - almost 100%. So there's nothing surprising about it.

But he obviously didn't play that many hands, so to know the odds of it happening, we'd need a sense of the total number of hands, or at least, the number of hours spent playing each time (from which we could estimate the number of hands). If P is the probability of hitting the hand, and N is the number of hands played on a trip, then the likelihood of hitting the hand at least once in the trip =

1-((1-P)^N)

You would need to calculate that for each trip, the multiply the probabilities together to determine what the odds were, before you went on the first trip, of having it happen at least once on both trips.

I also looked at Wizard of Odds, and on the page dedicated to Fortune side bets and paytables, the probability of the straight flush is listed as:

P = 0.00119787

That actually works out to about 1 in 834.8. Not sure if Wizard of Odds has a conflicting number elsewhere on the site - but for the purposes of this discussion, I'm going to use this one.

Let's assume that on both trips, you played for 8 hours each. For a full table, 30 hands per hour is reasonable, since it can be such a slow game. 240 hands per trip.

First trip = 1-((1-0.00119787)^240) = 0.2499 ~ 25%
Second trip = same thing ~ 25%

So, the odds of hitting that hand on each trip was about 25%. The odds of hitting it on two trips in a row are 25% X 25% = 6.25%

All numbers are based on the assumptions made - subject to change.

 

We'd need to know exactly how many hands you played on each trip to give you correct odds.

 

Interesting.

I really have no idea how many hands I played but I would say about 5 hours at each property would be pretty accurate

 

I think Polemarch's estimate of 30 hands per hour is pretty close. So 6% or something for the two trips. A lot easier than winning the lottery. His number of 1/834 is correct.

I had two straight flushes in two days on a trip to Florida playing Pai Gow Poker. But I hadn't had any for a couple years before that.


Off the subject, but one oddity of Pai Gow Poker is that it is substantially easier to get a straight than 3 of a kind (because of the Joker, mainly), but a straight is a better hand in the main game. (7.3% vs. 4.8%).

We had a great dealer error situation around this where the dealer ended up with a flush and a pair, but she ended up paying/pushing all the hands like we were playing 3-card poker! So the 3 of a kinds were beating the flush and the straights were beating the flush. Everyone at the table was appropriately quiet and they didn't discover the error. One funny part is that both suits ended up helping the dealer set her hand (she had a full house in combination with the flush, so there was a couple ways that looked plausible), but as soon as they figured out the right way, they left and she proceeded to make errors in the player's favor on 4 of the 6 hands.