View Thread : Blackjack Payout over 100%?


cbergstr
I was reading about this three 7 of spades Blackjack bonus put out by some casinos mentioned in ch4nce.com (http://www.ch4nce.com/story/2005/3/10/62349/8707).

Here's the deal. If you get three 7 of spades, they give you $5,000. I know that Blackjack usually has pretty good odds. My question is this... Does this three 7 of spades push the payout into the promised land (over 100%)?

Odds of getting three 7 of spades: 1/(52 x 52 x 52) = 7e-6 (yup, pretty small)
Payout: $5,000

Payout per hand: = payout x chance of getting payout = $5,000 x 7e-6 = 0.035 dollars = 3.5 cents.

This doesn't sound like much, but if you play 25 cent hands, it increases the payout by 14%! This means that the payout becomes over 100% and if you play long enough, you'll come out ahead.

Am I right?

GrandMaster
The probability of getting three 7 of spades depends on the number of decks, the more decks the better. For 8 decks the probability is 8x7x6/(416x415x414)=0.0000047, so the expected payout is only 2.35c assuming that you always hit a pair of 7 of spades and that the dealer does not peek for blackjack. I have not checked it in detail, but I think even when playing 25c hands you should follow basic strategy with a pair of 7 of spades, i.e., split them if the dealer is showing 2-6, hit them otherwise, which reduces the value of the extra payout to about 1.5c. Your expected hourly win would be around the minimum wage, but you would need to play millions of hands to be reasonably certain of making money.

bonuslover
GM, just wondering
do you have a CPU up in your head?
my guess is you have a P4 dual core