A shuffle through the gaming mailbag

Q. You've written about the Martingale system, where you double up your bets after losses, and said that it's bad for gamblers. I just heard about a different system, called the anti-Martingale, where you double your bets after wins.

You pick a number of wins you're going for. I bet on red or black in roulette, and decide to go for four wins. I bet $5, and if I win the first, I bet $10, then $20, then $40. If I win my $40 bet, I go back to a $5 bet and start again.

That way, I never risk more than $5 of my own money. My bigger bets are all with the house money, and I can get some nicer wins than if I just bet $5 every time.

A. The anti-Martingale isn't as dangerous as the Martingale. You're not risking hundreds or thousands of dollars at a time, as can happen to a Martingale player on a losing streak. But the anti-Martingale doesn't really work, either.

For starters, every dollar you risk is your money. Once you've won it, it doesn't belong to the house anymore. You can bet it if you want to. You also can cash it out and use it toward dinner, a show, bills, put it in the bank — whatever you want. It's your money, not house money.

As for the system itself, it will spot the house the same 5.26% edge on your red/black bets as any other wagering system.

In your four-win anti-Martingale, anytime a win is followed by a loss in any of the next three spins of the wheel, you'll wind up worse than a player betting a flat $5 a spin. If a $5 win is followed by a $10 loss, you have a net loss of $5. If a $5 win and a $10 win are followed by a $20 loss, you have a net loss of $5. If wins of $5, $10 and $20 are followed by a $40 loss, you have a net loss of — yes — $5.

If another player betting a flat $5 spin follows a $5 win with a $5 loss, he breaks even. If two $5 wins are followed by a $5 loss, he has a net profit of $5. And if three $5 wins are followed by a $5 loss, he has a net profit of $10.

It's a lot more common for a four-spin sequence to include a loss than for all four to be winners. The break-evens and small wins for the flat bettor offset the bigger wins with more frequent small losses for the anti-Martingale bettor. In the long run, the house will claim 5.26% of the action from either style of wagering. But bigger wagers mean the anti-Martingale bettor will contribute more dollars to the casino's bottom line.

Q. Now that so many casinos give free play for slot points instead of cash back, what is that actually worth? When it was cash back, I'd sometimes just let it accumulate until I was ready to leave, and then have that for pocket money on my way out the door. If I had $20 in cash back, I'd at least have 20 bucks to leave with. Now I have to play it through before I can cash out.

A. The value of free play depends on the game you play. If you load $20 in free play onto a penny slot machine that pays 88%, and make the required $20 worth of wagers, then on the average you'll wind up with $17.60. If you load $20 in free play onto a 9/6 Jacks or Better video poker game that returns 99.5% with expert play, then on the average you'd wind up with $19.90 if you play at expert level.

That doesn't mean you'll get back $17.60 every time you play that penny slot or $19.90 every time you play 9/6 Jacks or Better. The majority of sessions will be bigger losers, and you'll leave with less money than that. It's even possible to leave with zero, though that's not common. On a smaller number of sessions, you'll leave with more than $20, and maybe even hit a sizable jackpot.

If your goal is to leave with as much of the $20 as possible without worrying about either entertainment value or jackpot possibilities, your best bet is to seek out low-volatility games. Jacks or Better video poker and Bonus Poker, games where two pairs pay 2-for-1, are strong contenders to meet that goal.

Look for John Grochowski on Facebook (http://tinyurl.com/7lzdt44); Twitter (@GrochowskiJ) and at casinoanswerman.com.