Baccarat: Probability of a 3 card player 7 point hand with a 3 card banker 6-point hand

Baccarat: Probability of a 3 card Player 7-point hand with a 3 card Banker 6-point hand.

Good day to all, an online casino I recently come across has a promotion where if you bet on Player in Baccarat, and the outcome is a 3 card Player 7-point win over a 3 card Banker 6-point hand, you get a small cash reward. Naturally this led to the question where one might ask, what is the probability of such an outcome in a given hand? My gut tells me its probably something like 1 in 500 hands, but knowing the exact probability would be ideal of course. Thanks for any input, happy new year to all.

The probability is exactly 17,668,843,664 / 6,508,331,087,895,
or about 1 in 368.35 hands

Thank you sir for the information, given the minimum bet of $100, i think there is no value for the promotion. Thanks once again sir.

Quote: infiltratioz

Thank you sir for the information, given the minimum bet of $100, i think there is no value for the promotion. Thanks once again sir.
link to original post

What was the ‘small cash reward’?

It is $200.

Quote: ThatDonGuy

The probability is exactly 17,668,843,664 / 6,508,331,087,895,
or about 1 in 368.35 hands
link to original post

ThatDonGuy,

For 8 decks, I get the same probability, but my fraction is 13,569,671,933,952/4,998,398,275,503,360 = 0.002714804, or 1 in 368.3507088 hands. My denominator is 416*415*414*413*412*411, or roughly 5 x 10^15. How is your denominator of 6.5 x 10^12 so much smaller?

Dog Hand

Quote: DogHand

Quote: ThatDonGuy

The probability is exactly 17,668,843,664 / 6,508,331,087,895,
or about 1 in 368.35 hands
link to original post

ThatDonGuy,

For 8 decks, I get the same probability, but my fraction is 13,569,671,933,952/4,998,398,275,503,360 = 0.002714804, or 1 in 368.3507088 hands. My denominator is 416*415*414*413*412*411, or roughly 5 x 10^15. How is your denominator of 6.5 x 10^12 so much smaller?

Dog Hand
link to original post

Mine is in lowest terms. Divide your numerator and denominator by 768 to get mine.

Quote: infiltratioz

It is $200.
link to original post

As you’ve probably already determined, this 2-bet bonus adds a little over 1/2 of a percent to the remaining value of the play. (0.5430%)