Discount Gambling

For anyone interested in grinding out a profit from Triple Attack Blackjack, I thought I’d post a few graphs showing the distribution of outcomes for playing 100 shoes. I assumed a penetration of 7/8ths of the shoe, and for a heads-up player shamelessly betting 10x/20x when the Ace count is good, but otherwise playing basic strategy. These graphs should not be used to estimate bankroll requirements, but just give an idea of what to expect in the medium-run, and what kind of average profit rate to expect.

For a 10x big bet when the Ace count is good (+2 after 2 decks):

Cumulative Distribution of 100 Shoe Session Outcomes, 10x Bet for +EV Ace Count

Note the bias in the distribution clearly favors the player counting Aces. The x-axis is the net win/loss in small (1x) bets. The curves clearly cross the 50% cumulative frequency in positive net territory.

For a 20x big bet when the Ace count is good (+2 after 2 decks):

Cumulative Distribution of 100 Shoe Session Outcomes, 20x Bet for +EV Ace Count

Of course, you can also see the potentially large swings, which discourages all but extremely serious gamblers from trying this sort of thing. For example, varying your bet 20x against a unit $5 minimum bet means betting nickels when the count is bad, and black ($100) when the count is good. Over a 100 shoes, there’s a 10% probability of ending up stuck $6000 or more. Of course, there’s a greater chance of winning $6000 or more, and you’ll “average” a win of (250 units)($5/unit) = $1250 for this 100 shoe “session”.

In the next post, I’ll compare Triple Attack to normal 6-deck blackjack, showing how much more effective counting is, as far as shoe games go.