Odds of Dealer and Player getting Mini Royal in 3 card Poker

Hi,
A question open to anyone.
What would the odds of the dealer and player each hitting a mini-royal in '3 card poker' with 1, 6 or 8 decks.

I'm asking because I think it would be a pretty good side bet if the house was willing to stump up a decent payback.

Pretty sure TCP is only ever played with 1 deck.
But the odds would be astronomical. Too high to be a good side bet.

Three card poker.
Odds of a mini-royal = 0.000136. (.0136%)
squared = ~0.000000018 or about 1 in 54,065,744
Not one in a million, one in 54 million.
quick & dirty.

Quote: Paigowdan

Three card poker.
Odds of a mini-royal = 0.000136. (.0136%)
squared = ~0.000000018 or about 1 in 54,065,744
Not one in a million, one in 54 million.
quick & dirty.

Exactly. The payout could be 50million to 1. But who would play it? They could just offer $1000 to all players at the table if this ever occurs, and it would probably reduce the house edge by 0.0001%?

The hands are dependent, no? Wouldn't the odds change slightly since the removal of the cards making up one of the royals improves the chances for the second?

Quote: Ayecarumba

The hands are dependent, no? Wouldn't the odds change slightly since the removal of the cards making up one of the royals improves the chances for the second?

That occured to me, also, and I think you are correct. But Dan did say "quick & dirty."

I get the odds of 1 mini royal at 12/52 x 2/51 x 1/50 or, 1 in 5525
Once you have one mini royal the odds of a second one are 9/49 x 2/48 x 1/47, or 1 in 6141.333
So the odds of 2 minis using 2 defined hands (dealer's and yours) are 1 in 33,930,865 (rounded)
This is all assuming a single deck game.

Thanks so much.

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Quote: SOOPOO

I get the odds of 1 mini royal at 12/52 x 2/51 x 1/50 or, 1 in 5525
Once you have one mini royal the odds of a second one are 9/49 x 2/48 x 1/47, or 1 in 6141.333
So the odds of 2 minis using 2 defined hands (dealer's and yours) are 1 in 33,930,865 (rounded)
This is all assuming a single deck game.

First mini-royal is 4/combin(52,3). Second mini-royal is 3/combin(49,3). The probability of two mini-royals is (4*3)/(combin(52,3)*combin(49,3)) = 1-in-33930866.6666....

Just thought that this might be a more intuitive calculation.

--Ms. D.

A new way to express odds of an event taking place: Caesars has that One Million Dollar TCP Six Card bet.

They didn't indicate anything about house edge or odds or whatnot, they just said that their mathematician friends had told them they would most likely be paying out that million dollars three times a year. So I wonder: three days out of 365, then take all their tables for all shifts that day, then take the average Hands Per Hour for that day and eventually you could work your way to a pretty good estimate. Or perhaps "this bet should pay off big three times a year" is a good, if somewhat novel, way of expressing the odds of an event taking place.

I wonder which is a more sensible and understandable way of expressing it since many of the players will be ignorant of both the game and mathematics and also might be a bit soused as well?