1) Bet on Banker. Of hands which don't "push," Banker should win 50.66 percent -- a bit over half -- and lose 49.34 percent. The catch? The casino takes a fee, normally 5 percent of the proceeds. Per dollar bet, winners get only $0.95. The commission gives the house a moderately-low statistical edge, 1.21 percent.
2) Bet on Banker with side action on Tie. Chances of winning on Banker can be enhanced with an auxiliary bet on Tie. Say, $2 on Tie for $10 on Banker. Banker should come through on 45.8 percent of these combined wagers. When it does, bettors net $7.50 -- $9.50 for the $10 on Banker minus $2 on Tie. Tie should occur on 9.6 percent of these joint wagers. When it does, profit is $16 for the 8-to-1 payoff on Tie with no action on Banker. In all, the linked bet should win 55.4 percent of the time, yielding $7.50 or $16. The downside? Losses, whose probability is 44.6 percent, cost $12. And house edge is 3.2 percent.
3) Bet on Player with side action on Tie. Augmenting Player with Tie can shift odds to favor bettors. Assume $10 on Player and $2 on Tie. Player should hit 44.6 percent of these wagers, netting $10 minus $2 or $8. Tie, with 9.6 percent chance, yields $16. The combination should therefore win 54.2 percent of the time and return either $8 or $16. The bad news? Losses, with 45.8 percent likelihood, cost $12. And edge is 3.3 percent.
4) Group bets on Banker into five-hand rounds, doubling after every loss until a win occurs or the fifth wager goes down. Bettors have 97.1 percent chance of winning each round, while house edge is a mere 1.21 percent. The drawback? Earnings of 20 to 95 percent of the initial wager for losses 31 times this base. Starting at $10, this means risking $310 to make $2 to $9.50.
5) Group bets on Player into five-hand rounds, doubling after every loss until a win occurs or the fifth wager goes down. Here, bettors have a 96.7 of winning each round, with house edge of only 1.32 percent. The flaw? Profits equal to the initial bet for losses 31 times as high. For example, risking $310 to earn $10.
6) Group bets on Tie into eight-hand rounds, repeating after every loss until a win occurs or the eighth wager goes down. This sequence offers a 55.4 percent chance of earning from one to eight times the per-hand bet. The price? A 44.6 percent chance of an eight-unit loss, with house edge usurious at 13.6 percent.