A shuffle through the Gaming mailbag:

Q. I read something you wrote about doubling down on soft 17 vs. the dealer’s 3, 4, 5 or 6, and something about it just seems off kilter to me.

In every case, you said the average profit per dollar of your original wager when you doubled was very nearly twice the profit when you hit. For Ace-6 vs. 3, for example, you listed the average profit for hitting as 2.9 cents per dollar, and for doubling as 5.7 cents per dollar of your original wager.

You can break that down as 2.9 cents on your original bet and 2.8 cents on the double down.

So there is only a loss of a tenth of a cent for giving up the chance to hit if you get a bad card? Surely there has to be a bigger penalty than that for all those times you draw a 9 and turn your soft 17 into hard 16 and can’t hit again.

A. When we double on soft 17, we don’t run into very many situations in which we could hit again given the chance.

You listed Ace-6 vs. 3, so let’s break that one down for each possible card you could draw on your double:

Draw an Ace, you have soft 18, basic strategy play is to stand.

• 2 gives you soft 19, best to stand.

• 3 gives you soft 20, best to stand.

• 4 gives you soft 21, best to stand.

• 5 gives you hard 12, best to hit.

• 6 gives you hard 13, best to stand.

• 7 gives you hard 14, best to stand.

• 8 gives you hard 15, best to stand.

• 9 gives you hard 16, best to stand.

• 10 gives you hard 17, best to stand.

There is only one draw — the 5 that gives you a hard 12 — that would lead you to take another card if you were allowed unlimited hits. When the dealer has a 4, 5 or 6, you don’t even hit the hard 12s. In those cases, the differences between doubling down and twice the profit for hitting are just a matter of rounding.

Q. I’ve been playing craps all my life, and never really thought about put bets and taking odds, so I’ve found those entries really interesting. Honestly, I never even knew you could bet pass after the comeout and take odds.

What was striking to me was how much odds you need to overcome not getting the comeout. Trying to get under a 2 percent house edge takes you to 10x odds on 5 or 9 and 16x odds on 4 or 10? Forget it. I almost never play anywhere that give you those odds.

Even on 6 or 8, it takes 5x odds to make put bets as good as place bets.

So at tables that offer single odds or double odds, you should just put the put out of your mind, right?

A. You’re right. The smallest common odds that make put bets realistic choices are the 3x, 4x, 5x odds tables that are fairly common now. They give you the 5x odds on 6 and 8, but even 5x odds just puts the put on a par with place bets on 6 or 8. To make put plus odds better, you need more than 5x odds.

Also consider the size of your investment. If the pass minimum is $5, the 5x odds take your total investment to $30. At the same table, a place better can get the same 1.52 percent edge for $6, making placing 6 or 8 a better play for those of modest means.

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