Doubling your money in one bet

Jack is a blackjack player I've run into a few times as I make my rounds at casinos in my area. He loves to talk the game, but he also knows I don't like to talk odds and strategy while I'm playing.

"It's almost lunch time," he said one day just as I'd been dealt my third consecutive 14. "Want to take a break?"

Sure, I said. I had a couple of buffet comps, and offered to use them. Jack had bought lunch when he had couple of basic strategy questions the last time we met.

Plates full and beverages already at the table, we sat down. I asked Jack what was on his mind.

"I went online and reread your column about doubling your money in one bet," he began. "Not that I'd want to play that way --- foolish to risk your whole bankroll in one bet.

"But it got me to thinking. You say that you win more than half of decisions on the banker bet in baccarat. But what about some of the other games? It has to be close for a blackjack player."

Let's be clear on baccarat to start with. The banker bet wins more often than it loses. Banker wins 45.9 percent of hands, player wins 44.6 percent, and 9.5 percent are ties. If you leave your money on the table on the ties until you either win or lose, you'll win about 50.7 percent of all wagers.

"But the house keeps the edge by charging a 5 percent commission on winning banker bets," Jack piped in. "I understand that. So what about other games? Blackjack, craps, roulette. Especially blackjack."

Blackjack is another game with a fair amount of pushes, I explained. In a common six-deck game, if you play basic strategy, you'll tie the dealer and get your money back about 8.9 percent of the time. You'll win a shade over 43 percent, and lose a shade under 48 percent.

"And what if you keep the bets you push in play?"

You'll win about 47.5 percent, and lose about 52.5 percent. You lose more hands than you win, where in baccarat with the banker bet, you win more than you lose.

"And yet the house edge is lower in blackjack, or so you keep telling me."

Right. That's because in blackjack we get paid 3-2 on our two-card 21s, and have the option of splitting pairs and doubling down. Bottom line is that a blackjack basic strategy player can get the house edge down to about half a percent, give or take a few tenths depending on house rules. Bet on banker in baccarat, and the house edge is 1.06 percent if you consider ties a final outcome, or 1.17 percent if you assume all hands will be played to a win-lose decision.

"OK, a basic strategy player can't win more hands than he loses. What about a card counter?"

They narrow the gap a tiny amount, but they win money not so much because of playing decisions, but because they bet more when the remaining deck is in their favor, and less when it's not. If remaining deck has a high concentration of 10s and Aces, then there will be more blackjacks. Players are paid 3-2 on blackjacks, and the house isn't. Also, in a double down situation, you're more likely to get a 10 and make your 20 or 21 if the remaining deck is rich in high cards.

"But card counters still lose more hands than they win?"

Right.

"Craps, then. What about the pass line? That's, what, a 1.4 percent house edge?"

Close enough, 1.41 percent. There are no pushes on the pass line, so that's straightforward enough. You lose 50.7 percent of trials, and win 49.3 percent.

"But with say, 100 times odds, the house edge is lower even than in blackjack."

Yep, all the way down to 0.02 percent with 100 times odds. The free odds are paid at even money, lowering the house edge of a pass-odds combination. But you can't bet the free odds by themselves. Taken with the pass line, you still lose 50.7 percent of wagers.

"Roulette?"

The most frequent winners are the bets that are paid at even money --- red or black, odd or even, 1 through 18 or 19 through 36. Just divide the 5.26 percent house edge in half and add the result to 50 percent --- 52.63 percent of spins are losers, 47.37 percent are winners.

"That's not far under the 47.5 percent winning hands at blackjack."

Right, but there are no 3-2 blackjack payoffs, or splitting pairs or doubling down in roulette, so the house edge is much higher.

"Sounds like if I want better than a 50-50 chance of winning one bet, I still have to stick to baccarat."

Sure. Is that what you want?

"Not necessarily," Jack said with a grin as he finished his lunch. "I want a better shot at their money. It doesn't have to be one hand. Back to the blackjack table."