house advantage in northeast Penn.

I play 6d, das, s17, resplit to 3 hands, late surrender. $5 table is available with csm. If I bet $7.50 so that the bj payoff is $11.50, will that give me an advantage over the house?

Richard,

The house edge for your game is 0.34%, so you would have to surpass that amount to have the advantage.

On a $7.50 bet, the normal return for a BJ is $11.25, so by getting $11.50 you're receiving a "bonus" of $0.25, which in terms of your initial bet is (+$0.25/$7.50)*100% = +3.3333%.

But how often do you collect the bonus? In a 6D game, the probability that you'll get a BJ can be calculated as follows.

BJ Prob = (Prob of Ace)*(Prob of X) + (Prob of X)*(Prob of Ace)

Where "X" is any 10-valued card.

Of course, the two terms on the right-hand side of the equation are equal, so instead we say:

BJ Prob = 2*(Prob of Ace)*(Prob of X)

Since a 6D shoe contains 312 cards including 24 Aces and 96 X's, we get:

BJ Prob = 2*(24/312)*(96/311) = 0.047489..., or a bit over 4.7% of the time.

But wait, there's more! To get the bonus, you need to get a BJ without the dealer also having a BJ. The untied BJ Prob is given by

Untied BJ Prob = 2*(24/312)*(96/311)*(1-2*(23/310)*(95/309)) = 0.045322..., or a bit over 4.5% of the time.

In this equation, the term "2*(23/310)*(95/309)" is the dealer's BJ Prob given that YOU already have a BJ, so "(1-2*(23/310)*(95/309))" is the dealer's probability of NOT having a BJ given that YOU have a BJ.

So, the net effect of the Bonus is to give you a bonus of +3.3333% a bit over 4.5% of the time. Multiplying these percentages gives you a bonus of +0.15107...%, which is insufficient to overcome the house edge of 0.34%, though it does reduce it quite a bit.

Hope this helps!

Dog Hand

... you are the one who writes and thinks almost exactly the way I do!

I'll leave it to others to decide if that's a compliment or not (!), but it was meant to be.

Don

Some mini-casinos in Washington have $2.50 checks for paying off those pesky bj's on $5 bets.

when he uses Late surrender like the tribes do in Conn.

for blackjacks and late surrender.I think the Woods short pays, as I have not been there for a while.

Thank you Dog Hand for your detailed analysis of house advantage in Northeast Penn.

2.50 chips available in NE Pa.