Deal Me In: The oddities of odds

Dear Mark: Seems to some of us that the replacement discard is the same face value card but a different suit (of course) than random probabilities would warrant. Example: I discard a six of clubs and a six of another suit appears in its place more frequently than one would expect. Bob W.

For openers, Bob, let’s get right to the math. Say for instance you have a 6-J-Q-K-A of mixed suits, and you discard the six. Up to this point you have had a peek at five of the 52 cards in the deck, leaving 47 possible draws, with three of those remaining cards being sixes. When you’ve discarded the dealt six, your chances of drawing another six are three out of 47 or 6.4 percent. I wouldn’t call 6.4 percent of the time an off-chance fluke.

What I believe is happening psychologically, Bob, is that you are streaking an anomalous amount of sixes, which sometimes spawns a “what the hell is going on here” frame of mind – like my own thoughts today with eight inches of snow on my doorstep. Extend your video poker timeline and the odds of getting the same denomination card on the draw, 3 in 47, should fall into place. And my snow will melt.

Dear Mark: I have heard that you should always stand on all 17 and 18 hands no matter what the dealer shows. Is that true? Also, I have always wondered why basic strategy charts instruct you should double down on 11 against all dealer face-up cards in a single-deck game, but not against aces in multi-deck games. Aaron G.

Not so, Aaron, standing on all 17s and 18s. You’ll note that the basic strategy charts you referred to in your question affirm that if your hand contains an ace for a soft 17, you are supposed to hit it, not stand. As for a soft 18, again you hit, unless the dealer has a 2, 7 or 8 showing.

As to the second part of your inquiry, why double on 11 against an ace when one deck is being used, but not on multiple-deck games, is baffling for some players.

What they might not realize, Aaron, is that any time you play single-deck blackjack, every card dealt has a greater effect on the balance of the remaining cards in the deck single deck, than it would have on multiple decks.

For example, if you have a seven and a four for a two-card 11, and the dealer shows an ace, then 16 of the remaining 49 cards in a single deck are 10-values that would give you 21. That’s 32.7 percent versus 31.1 percent (96 of 309 cards) on a six-deck game.

By the way, Aaron, since we’re talking single deck, blackjacks, which pay 3 for 2 (a payoff of $3 for every $2 wagered), occurs more frequently on a single-deck than on multi-deck games. To illustrate this, let’s say your first card is an ace. On a single deck game, 16 of the remaining 51 cards, or 31.37 percent, are the face or 10-value cards that would complete your blackjack. On a six-deck game, 96 of the remaining 311 cards, or 30.87 percent, would give you your blackjack.

Oh, and one more thing, Aaron. If you do stumble upon a rare single-deck blackjack game, make sure you are getting the maximum value for a blackjack, one that pays 3 to 2. Seems most single-deck games today are 6 to 5 games, with a whopping house advantage of 1.45 percent.

Gambling Wisdom of the Week: “You may have luck for an hour or two, even a day or two, even a week. But what people call luck is merely an established fact seen through the spectacles of after events.” —Nico Zographos, renowned 1920s and 30s baccarat gambler