I�ve got an idea how to beat a local blackjack game playing basic strategy and using a bonus offer. The game is European (no hole card) 6-deck blackjack, but the rules are good - dealer stands on soft 17, double on any 2 cards, double after split, resplit aces, early surrender versus 10. The house edge is about 0.24%, but to be conservative let me round it to 0.5%. At the moment there is the following bonus running: if one places a 10 unit bet and receives as an initial hand a pair of sevens he is entitled to 50 units in free bets. The player may use the free money as he pleases, but to be able to cash the money out he must increase it in amount to 100 units at least. The probability of getting a pair of sevens for 6-deck game is about 0.54%. The above percentage shows that from every 185.2 initial hands there should be one with a pair of sevens. I�ll round 185.2 to 200. Thus, for every 200 initial hands of 10 units the basic strategy player will lose 200*(10/0.76)*0.005=13.16 units. I divide 10 by 0.76 to include extra money on doubling and splitting. On the other hand, for every 200 hands, on average, the player will be rewarded with 50 units free money. If one places all the 50 units on the next hand and win he will turn the money into 100 units. Thus he will be able to cash the 100 units out. When betting with free money one can neglect surrendering, splitting and doubling options and still should be able to win about 45% of these hands excluding ties (100%=45% winning hands + 55% losing hands). Here are the calculations:
A dream-come-true. But what about the standard deviation? One could lose much more than just 13 units for 200 hands and could wait much longer than 200 hands for a pair of sevens. And he could lose his first 5-6 free money bets. So, what is the worst I can expect? What amount of bankroll will I need and how long will I have to play to overcome the effect of standard deviation? It will be very kind if somebody gives me a piece of advice on this matter.