The basics of splitting 9s in blackjack

If you're a blackjack player, and have never looked at a basic strategy table, you should.

It's a tidy little grid, with possible player hands down the side, and possible dealer face-up cards across the top. Find the rectangle directly across from your hand, and directly down from the dealer's, and the basic strategy table tells you whether to hit, stand, split, double down or even surrender, if the house permits such a thing.

Mostly the plays fit into neat little groupings, as you can see if you check out charts such as those on Michael Shackleford's Wizard of Odds site, at http://wizardofodds.com/blackjack. Large blocks of hands have the same correct play. If you start with a pair of 7s, the block of rectangles showing dealer up cards of 2 through 7 tell you to split the pair, while the block showing dealer's 8 or above tell you just to hit. Sometimes the block of like plays comes in the middle of the line. With Ace-4 or Ace-5, the grid tells you to double down in that block showing dealer's 4, 5 or 6, but just to hit against anything else.

Basic strategy is orderly and logical. The charts don't tell you to make one play against one dealer up card, the opposite play against the next higher card, then go back to the original play against the next cart.

Except....

Yes, there is an exception to all that orderliness. When you have a pair of 9s, the blocks aren't quite so neat. Sure, there's a big block that tells you to split the pair. Whenever you have a 2 through 6, the chart tells you to split. But when you have a 7, it tells you to stand. Then it says to go back to splitting if the dealer has an 8 or 9, and back to standing against a dealer's 10-value or Ace.

Those back-and-forth-and-back shifts are unique on the basic strategy table, and worth thinking about.
The hands to focus on are those three rectangles that tell us just to stand on our pair of 9s. We stand when the dealer has a 7, and we stand when the dealer has a 10-value or an Ace. What the basic strategy chart is telling us is that in blackjack, sometimes we play offense, and sometimes we play defense. Sometimes our object is to maximize winnings, and sometimes our object is to minimize losses.

If you start with a pair of 9s and the dealer has a 7, you have an edge. Your 18 will win whenever the dealer has a 10-value --- 10, Jack, King or Queen --- face down, and it will push whenever the dealer has an Ace face down. Four of the 13 denominations in the deck turn your 18 into an instant winner, and there are no cards that turn the dealer's 7 into an instant winner against you. If the dealer is going to win the hand, he or she is going to have to draw. Standing pat is your best offense in that situation. You have the edge, so keep it.

But if the dealer has a 10-value or an Ace, you have no such edge. Your 18 will lose more often than it wins. Splitting the pair and starting each hand with a 9 doesn't help. It just leaves you with two hands that lose more often than they win. And splitting the pair means making a second wager, so you have more at risk.

Time to play defense. We stand on the 9s when the dealer shows a 10-value or Ace because we don't want to make a second bet and increase our risk.

So we play that little game of back-and-forth-and-back on the basic strategy chart. Dealt a pair of 9s, we play offense and maximize our potential winnings by standing when the dealer shows a 7, and we play defense, minimizing losses, when the dealer has a 10-value or Ace.

All very neat, don't you think?

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Speaking of blackjack basic strategy, a caller recently asked why basic strategy charts say you should double down on 11 against all dealer face up cards in single-deck games, but not against Aces in multiple-deck games.

The reason is that in single-deck blackjack, each card dealt out has a greater effect on the composition of the remaining deck. If you have a 6 and a 5 for a two-card 11, and the dealer has an Ace, then 16 of the other 49 cards in a single deck --- 32.7 percent --- are 10-values that will give you 21. In a common six-deck game, it'd be 96 of 309 cards, or 31.1 percent.

You have a better chance of winding up with a strong hand when you double down in a single-deck game. That's why you double on 11 against an Ace when one deck is being used, but not in multiple-deck games.

Readers ask about other blackjack players, and loosening the slots

Question. What percentage of blackjack players do you think are counting cards? Half? I just wonder, when I see players splitting 6s against a 10. They can't be counting cards.

Answer. I doubt that half of blackjack players in casinos have studied a basic strategy chart, let alone count cards. I'd put the number of card counters at less than 1 percent of the blackjack-playing population.

Before any player who is trying to get better worries about counting cards, he or she must master basic strategy first. An average blackjack player faces a house edge of about 2 to 2.5 percent. Learning basic strategy can cut that house edge to around a half percent or less, depending on house rules.

How can you tell if someone at your table is a basic strategy player? Here are a few common moves that separate those who know their basic from those who don't:

• A basic strategy player hits hard 16 when the dealer shows a 7. Every time.
• A basic strategy player splits Aces, and splits 8s, even when the dealer has a 10 face up.
• A basic strategy player never stands on soft 17. He or she hits or doubles down, depending on the dealer's face up card.
• A basic strategy player hits on 12 if the dealer shows a 2 or a 3.
• A basic strategy player hits on soft 18 if the dealer shows a 9, 10 or Ace.

Those are all moves that give trouble to those who play by intuition.

Card counters will sometimes make plays that run counter to basic strategy. In addition to hitting 12 against a 2 or 3, a counter will sometimes also hit 12 against 4, if the composition of the remaining cards is right. A card counter also will sometimes hit 16 against 10, but not 16 vs. 7.

Insurance is a special case. Intuition players often will insure their blackjacks by taking even money when the dealer has an Ace face up. Basic strategy players will never take insurance --- that's the right play most of the time. Card counters, on the other hand, will take insurance if the remaining deck includes a high enough percentage of high cards.

Look around next time you play. See how many players hem, haw and sometimes stand on 16 vs. 7, or fail to split 8s against a 10, or stand on Ace-7 against a 9. That'll tell you just how few basic strategy players there are --- and there are many, many few card counters.

Question. I would like to know if adding say $1,000 to a slot machine loosens that machine for a big payout.

Also, I always play the max. Does it matter what the denomination of the game is? That is, do the games loosen as the denomination rises? Does a $1 game pay more than a penny slot played at maximum?

Answer. No amount of play changes the odds of hitting a winning combination on slot machines. If the game is programmed so that there is a 1 in 10,000 chance of hitting the big jackpot, then there is a 1 in 10,000 chance on every spin. If you've just hit the jackpot, the odds are still in 1 in 10,000; if you've played 9,999 spins without hitting the big jackpot, the odds are STILL 1 in 10,000.

(The 1 in 10,000 is just an example, by the way. Some machines hit more frequently, some much less. There are machines with a 1 in 2,000 chance of hitting the top jackpot, while in a big-money game like Megabucks the chances are 1 in tens of millions.)

If it's a progressive machine, adding money to the top jackpot does not change the odds of your hitting that jackpot. If the progressive meter starts at $1,000, and the jackpot meter has grown to $2,000, the chances of winning are the same as when you started. The long-term payback percentage does grow with the progressive meter, because the big hit pays more when it finally comes.

As for changing coin denomination, that DOES make a difference. Generally, penny machines pay less than nickel machines, which pay less than quarters, which pay less than dollars and so on. If you play maximum coins on a penny machine, your bet may be as large as if you're playing a three-reel dollar slot, but in most cases the dollar game will have a higher payback percentage.

Of course, there's also a difference in the play experience between a penny video slot and a dollar reel-spinner. Winning spins are more frequent on the video game, but payoffs of many times your wager are more common on the reel-spinner. The penny game will keep you in your seat longer, but the dollar game gives you a better chance of walking away with a fairly substantial win. That's the choice slot players face when deciding between low-denomination video games and higher denomination reel spinners.

Splitting hairs in Caribbean Stud strategy

Q. Playing Caribbean Stud Poker, I had Ace-King-8-5-2, and the card the dealer turned face up from her hand was an Ace. I made the bet, because my Ace matched his Ace. Another guy at the table told me that was the wrong play, that you bet only if one of the other three cards matches the dealer. The dealer didn't qualify, so I won on my ante and just got my bet back anyway. Her next highest card was a 10, and there were no pairs. But was the other player right? I want to give myself the best chance to win, and I always thought I was doing it by betting with Ace-King and a match.

A. The other player was correct. When we have Ace-King in Caribbean Stud, we do a lot of splitting of hairs. One of those hair splits is that when we have Ace-King and no other face cards in the hand, we bet whenever one of the other three cards matches the dealer's face up card, and fold when there's no such match.

Note the provision that there are no other face cards in the hand. If we have Ace-King- Queen or Ace-King-Jack, we bet if any of our five cards match the dealer's face-up card, and with Ace-King-Queen, we bet even with no match if our fourth highest card outranks the dealer's up card.

How much does all that gain us? Very little. With the strategy given here, you'll face a house edge of about 5.23 percent of the ante or 2.56 percent of total action. According to Michael Shackelford's outstanding Web site, wizardofodds.com, if you bet with Ace-King when any of your five cards matches the dealer up card, the house edge is 5.33 percent of the ante or 2.62 percent of total action.

By far the most important component of Caribbean Stud strategy is to bet with all pairs. I've seen many players fold with a pair of 2s or 3s. Those aren't necessarily winning hands, but in the long run, you'll lose more money by folding and forfeiting your ante than you will by betting the hand and accepting that you'll win some and lose some.

With bigger jackpots, do four-Ace hands occur less often?

Q. How is it that a casino can afford to pay you 800 coins for four Aces on some games, 2,000 on some others, but only 125 on Jacks or Better? On the games that pay more, are they programmed so the Aces come up less often?

A. On the contrary. We hit four Aces more often, not less, on games such as Double Bonus Poker (800 coins for a five-coin bet), Double Double Bonus Poker (800 coins most of the time, but 2,000 if the four Aces are accompanied by a 2, 3 or 4) or Super Aces (2,000 coins) than we do on Jacks or Better (125 coins). That's because we adjust our playing strategy to account for the bigger payoffs on those Aces.

The prime example is a full house that includes three Aces. On Jacks or Better, we just take the full house payoff. On the other games mentioned, we hold the three Aces and discard the other pair, hoping for the fourth Ace.

So how can games such as Double Bonus, Double Double Bonus and Super Aces pay us so much more than Jacks or Better does on Ace quads? Because what they give you on four of a kind, they take away elsewhere on the pay table. One thing all those big Ace games have in common is that they pay only 1-for-1 on two pair, instead of the 2-for-1 you get on Jacks or Better. The drop in the two-pair payoff costs us about 12 percent of our return in the long run, giving game designers plenty of leeway to give us bigger bonuses elsewhere on the pay table.

Do casinos make their profit from winning players?

Q. Sitting in the buffet, I caught a snippet of conversation that I was wondering if you could explain. (I wasn't listening in, they were so loud I couldn't help hearing.) One guy was saying that the casino really makes its money off the winners, and the other guy said something like, "Oh really? You mean we pay for all this when we win?" That doesn't really make sense to me.

A. Kind of leaves you wondering what kind of gambling palaces they could build if everybody won, doesn't it? If the casino makes money off the winners, then more winners must mean more profits, right?

But seriously, there is a way of looking at how the casino makes its money that looks at casino profits as a tax on the winners. Casino games make money because they pay the winners at less than true odds. If 38 people are sitting at a double-zero roulette table and each bet $1 on a different number on a single spin, the 37 losers each will lose their buck, and the one winner will be paid at 35-1 odds and walk away with $36. If the casino was paying true odds, the one winner should be paid at 37-1 odds and walk away with $38. The casino profit is the $2 not paid to the winner that he'd get if true odds were paid.

Same deal with sports betting. In most sports books, you have to put down 10 percent vigorish on top of your bet. Let's say you and I are betting on the same football game, with me betting on Team A and you on Team B. We each intend to bet $100, but we have to pay the vig, so we actually each bet $110. When my team wins --- hey, it's my example; I get to win --- you lose your $110 bet, but I'm paid only $100, along with the return of my $110 wager. The casino profit is the $10 it didn't pay me on my winning bet.

Sometimes the paying of winners at less than true odds is disguised a bit. In baccarat, for instance, bets on banker win more often than they lose, and bets seem to be paid at even money. However, bettors have to pay a 5 percent commission on winning bets, so winners aren't really paid at 1-1; they're paid at (1 minus .05)-1, and that's less than the true odds of winning the wager.

So it goes with every casino game. There are going to be winners, and there are going to be losers, but the house will make money because it pays winners less than the true odds of winning the bet.