SomeSpaceGuy
Joined: Mar 5, 2018
• Posts: 2
March 5th, 2018 at 8:28:27 AM permalink
I am trying to calculate the probability and return of the BJ Perfect Pairs side bet for four and six deck shoes, using two pay different tables (30,10,5) and (30,12,5). I can confidently calculate the perfect pair (8*1)-1)/((8*52)-1)) = 0.016867..., but get stuck when calculating the mixed pair and pair. Also, I was wondering whether these calculations take into account the dealers first card (UK blackjack). Any help would be greatly appreciated.
gordonm888
Joined: Feb 18, 2015
• Posts: 3700
March 5th, 2018 at 9:42:44 AM permalink
Let's do this for a 4-deck shoe. After the first card has been dealt to you, 207 cards remain in the shoe.

Perfect Pair
No matter what your first card is, there are 3 cards out of 207 remaining in the shoe that will give you a perfect pair. So 3/207 = .014493

Colored pair There are 4 cards that will give you a colored pair. 4/207 = 0.019324.

Red/Black Pair. There are 8 cards of the same rank but opposite color. 8/207 = 0.038647.

To calculate the payback or house edge, you can ignore the dealer's upcard, because you have no prior knowledge of whether the dealer's card will improve or reduce your odds of winning the sidebet.

If you have a 9 of spades and the dealer's upcard is a rank other than 9, then your odds will be improved (in the 4-shoe example). To calculate those odds, calculate the above fractions with 206 cards in the denominator.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
SomeSpaceGuy
Joined: Mar 5, 2018
• Posts: 2
March 5th, 2018 at 10:35:00 AM permalink
Thanks man. I was just about to reply to my own question as I managed to get it. Where I was going wrong was when calculating the coloured pair and mixed pair, I was forgetting to remove the 3 cards that would make it a perfect pair instead of a coloured pair, and the 7 cards that would make it either a perfect pair or a coloured pair instead of a mixed pair.

Thanks for the clarification on the dealer's upcard.