I've just learned about the huge advantage a player can have if they can cut the deck accurately when bottom card is shown by the dealer. My question is this, can you use this information to cut yourself a face or the queen of hearts when playing the Lucky Ladies side bet and come out ahead? The reason I ask is that one of the casinos in town has LL on all of their BJ tables. I'm going to try and post some math to this, can someone please verify it for me?
Luck Ladies pays out as follows:
Qh & dealer has BJ 1000:1
Q of hearts pair 125:1
Matched 20 19:1
Suited 20 9:1
Unsuited 20 4:1
Non-20 -1:1
Ok, here goes:
Cutting yourself a Queen of Hearts:
While you are counting down the one deck you cut to the Qh, make sure there are no other Qh in the first 52 cards. If there are not, when you get your Qh there are (5 Qh left)/(260 cards left in the deck)
EV for pair Qh and dealer blackjack:
($-1*255/260)+(($1000*(5/260*0.0474895)) = $-.0675
Where .0474895 is the probability that the dealer has BJ.
EV for pair of Qh:
($-1*255/260)+($125*5/260) = $1.42
Total EV for cutting yourself a Queen of Hearts LL Side bet = $1.42 + $-.0675 = $1.35 (not sure on this total, can you just add EVs?)
Ok, so that looks ok but it's going to be rare that you can cut yourself a Qh. How about cutting yourself a face card trying to get another face card?
If you cut yourself a face, again I'm going to assume normal distribution of face cards through all 6 decks (to get an even greater edge, use card counting for the first deck if the count is positive faces aren't normally distributed).
In the 5 remaining decks, there are (80 face cards)/(260 total cards)
EV:
($-1*180/260)+($4*80/260) = $.54
Suited EV:
($-1*240/260)+($9*20/260) = $-.23
Same Card EV:
($-1*255/260)+($19*5/260) = $-.62
Total EV for cutting yourself a face card:
.54 + (-.23) + (-.62) = -.31
Please someone check over this math for me, I'd cut to a Queen hearts if these numbers are correct.
Josh
Luck Ladies pays out as follows:
Qh & dealer has BJ 1000:1
Q of hearts pair 125:1
Matched 20 19:1
Suited 20 9:1
Unsuited 20 4:1
Non-20 -1:1
Ok, here goes:
Cutting yourself a Queen of Hearts:
While you are counting down the one deck you cut to the Qh, make sure there are no other Qh in the first 52 cards. If there are not, when you get your Qh there are (5 Qh left)/(260 cards left in the deck)
EV for pair Qh and dealer blackjack:
($-1*255/260)+(($1000*(5/260*0.0474895)) = $-.0675
Where .0474895 is the probability that the dealer has BJ.
EV for pair of Qh:
($-1*255/260)+($125*5/260) = $1.42
Total EV for cutting yourself a Queen of Hearts LL Side bet = $1.42 + $-.0675 = $1.35 (not sure on this total, can you just add EVs?)
Ok, so that looks ok but it's going to be rare that you can cut yourself a Qh. How about cutting yourself a face card trying to get another face card?
If you cut yourself a face, again I'm going to assume normal distribution of face cards through all 6 decks (to get an even greater edge, use card counting for the first deck if the count is positive faces aren't normally distributed).
In the 5 remaining decks, there are (80 face cards)/(260 total cards)
EV:
($-1*180/260)+($4*80/260) = $.54
Suited EV:
($-1*240/260)+($9*20/260) = $-.23
Same Card EV:
($-1*255/260)+($19*5/260) = $-.62
Total EV for cutting yourself a face card:
.54 + (-.23) + (-.62) = -.31
Please someone check over this math for me, I'd cut to a Queen hearts if these numbers are correct.
Josh