Basic Blackjack Statistics

Numbers Don’t Lie

By Henry Tamburin

Dominator, who is my good friend and fellow blackjack instructor, will probably kill me when he reads this article. He’s always preaching to me that blackjack players "don’t want to know how the clock works, they just want to know what time it is, so don’t bore them with a lot of numbers." But I’ve decided to risk life and limb and discuss some of the more important blackjack statistics in my column this month, because I believe it helps players better understand the fundamentals of winning blackjack strategies. I’ve got to admit, however, that numbers are boring to most folks, so I crafted this article as a fun quiz (at least I hope you find it entertaining, as well as informative). So let’s get going, and Dom, if you are reading this …have mercy on me.

1. Ignoring ties, the percentage of hands that you can expect to win when you play blackjack is about:

a. 45 percent

b. 48 percent

c. 50 percent

Answer: b. When you ignore the 9 percent of the hands that tie, you can expect to win 48 percent of the hands dealt to you, and lose 52 percent. Notice that you will lose significantly more hands than you win. So how do you win money playing blackjack? For starters, the average amount of money that you win on the winning hands is slightly greater than a single betting unit because the latter are sometimes hands where you get a blackjack and are paid at 3-2, or you double down and win double the amount of your bet. Losing hands, on the other hand, often lose only a single betting unit. The result is that monetarily you will be close to, but not quite even when you play (this assumes that you use the basic playing strategy for all your hands). If you want to go a step further and win much more money on winning hands compared to the amount you will lose on losing hands, so that overall you show a gain, then you’ve got to learn card counting.

2. If you are dealt three consecutive hands, what is the chance that they will all lose, excluding ties?

a. 1 percent

b. 14 percent

c. 30 percent

Answer: b. You have about a 14 percent chance of losing three hands in a row when you play blackjack. Surprised? Most players probably guess 1 percent because they figure the chance of this happening is very low. Well it isn’t, so don’t panic and abandon the basic playing strategy when it happens.

3. How frequently does a player get a blackjack?

a. Once every 15 hands

b. Once every 21 hands

c. Once every 30 hands

Answer: b. The game is 21 and you can expect to get a blackjack once in every 21 hands. This brings me to the point why I harp that you should never play any blackjack game that pays 6-5, instead of 3-2, for a winning blackjack. Suppose you play two hours’ worth of blackjack on one of the heavily advertised, $10 minimum, 6-5 single deck games. Let’s assume you are dealt 100 hands per hour, so over the course of two hours you played 200 hands of blackjack. Getting a blackjack once every 21 hands means that you should theoretically have gotten about 10 blackjacks. Sometimes you’ll get more blackjacks in two hours of play, sometimes less, but on average you’ll get 10. Each of those blackjack hands cost you $3 on a 6-5 game (the difference between getting paid 3-2 vs. 6-5, or $12 instead of $15, for your $10 wager). So you forked over $30 to the casino for the privilege of playing a single deck game (yeah, right). Save your money and avoid playing any 6-5 single deck games.

4. How frequently does a basic strategy player bust?

a. Once every six hands

b. Once every eight hands

c. Once every ten hands

Answer. a. A basic strategy player can expect to bust about 16 percent of the time or once every six hands. When a player busts, he always loses. Not so with the dealer (see next question).

5. How frequently does the dealer bust?

a. One time out of every seven hands

b. Two times out of every seven hands

c. Three times out of every seven hands.

Answer: b. The dealer busts about 28 percent of the time, or about two times out of every seven hands. Unlike a player bust, the dealer often wins when she busts, because players who act first and bust automatically lose (this is how the house has a built-in edge in blackjack). The 28 percent is an average over all possible dealer upcards. In fact, the dealer will bust significantly more times when she shows a 2-6 upcard (about 42 percent with a 5 or 6 upcard), and much less with a 7 through Ace upcard (with an Ace, it’s only 17 percent after checking for a natural). Because the dealer’s chance of busting is higher when she shows a small upcard, you should not risk busting a 12-16 stiff hand and should always stand (with two exceptions - it’s slightly better to hit a 12 against a dealer’s 2 or 3). However, when the dealer shows a strong upcard from 7 though Ace and has a much lower risk of busting, you should be more aggressive and hit your stiff hands until your hand totals 17 or more (even if it means you risk busting).

6. You can expect your initial two-card hand to be a hard 12-17 about:

a. 30 percent of the time

b. 35 per cent of the time

c. 43 percent of the time

Answer: c. About 43 percent of the time you’ll be holding a 12 through 17, and the only way you can win is if the dealer busts, or you improve your hand. So any time you hold a 12 through 17 it’s bad news and you should expect to lose. In fact, approximately 85 percent of your financial losses occur with these hands. The best you can do when you are holding a 12 through 17 is to play your hand optimally using the basic playing strategy to minimize your losses.

7. The dealer has an Ace upcard. What is the chance she has a 10 in the hole for blackjack?

a. 15 percent

b. 24 percent

c. 31 percent

Answer: c. The dealer will have a ten four times out of 13, or roughly 31 percent of the time. The remaining 9 out of 13, or 69 percent of the time, the dealer won’t have a 10 in the hole. When you make the insurance bet, you are betting that the dealer has a ten in the hole when she shows an Ace. Assume you make a $10 insurance wager. Four times you’ll win $20 on the insurance bet (2 to 1 payoff odds) for a total win of $80. The other nine times you will lose $10 on your insurance bet for a total loss of $90. In other words, you lost more than you won. Therefore, it’s wise to never make the insurance bet.

8. The edge that card counters have over the casino is approximately:

a. 1 percent

b. 10 percent

c. 50 percent

Answer: a. Most players are surprised at the tiny one percent edge that card counters have over the house. Oftentimes, depending upon the game and the card counting system being used, the card counter’s edge is even less. With an edge this small, it means in the short run, luck will play a great role in the fortunes of a card counter, even though he will show a profit in the long-run.

So how did you do on the questions? It really doesn’t matter how many you got right or wrong, but whether or not I motivated you to play better. And I hope I did.

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Henry Tamburin is the Lead Instructor in the Golden Touch™ Blackjack course (www.goldentouchblackjack.com) and editor of the Blackjack Insider newsletter. For a free 3-month subscription to his blackjack newsletter with full membership privileges, visit www.bjinsider.com/free.