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Numbers Don’t Lie

In each hand, the probability of winning stands at 42.42%. Which means that in order for one to win 3 times in a row is. 42.42% x 42.42% x 42.42% = 7.63%. In the table below, the probability of the possible final hands that the dealer can have, according to the his up card is demonstrated. The odds of being dealt a natural blackjack are merely 4.8%. Following this chart you will see that the most common two card hand, at 38.7%, is a hand totaling 1-16, which is considered a decision hand. Dealer Final Hand Probabilities This blackjack odds chart shows the dealer final hand probability. A natural blackjack is only 4.8%, which essentially is an ace dealt with a ten card straight off the initial deal. Normally the odds are 3 to 2 and you would win $3 for every $2 wagered. It's a small percentage but it's the most desirable hand to get. The lowest hand you can get is two points (two aces).

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

Odds Of Winning Blackjack Hands In A Row One

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.

I had a look at the web site and also found what little he says about the theory behind his system makes it sound like card counting. However I'm deeply skeptical of anything that claims to 'blow old fashioned card counting away.' I think we can file this under 'If it sounds too good to be true is probably is.'
Update: The web site in question vanished sometime after the publication of this question.

I don't put a lot of emphasis on betting systems. In the long run you will lose the same percentage of money bet no matter what system you use. So my advice is use a system that maximizes the fun of the game.

Odds Of Losing 7 Blackjack Hands In A Row

The simple answer is no, it neither helps you nor hurts you. However, you will have less bankroll variance by betting two hands of x as opposed to one of 2x. Card counters are an exception to the simple no, they may play multiple hands to draw more cards out of a deck rich in good cards, thus improving their odds.

Thank for the compliment and I'm happy to help your bankroll last longer. When I gamble for fun I keep playing until it isn't fun any longer. Usually the fun ends when I have lost too much or have played too long. With the ups and downs of blackjack it takes hundreds of hours before regression toward the mean will cause actual results to look like expected results. Furthermore, the player who puts a conservative cap on their winnings is never going to experience the fun of a long hot winning streak. Keep in mind this is just what works for me. You should do what you are comfortable with. Everything I have to say about money management can be summarized by the following two rules (1) don't gamble with money you can't afford to lose, and (2) don't gamble if it isn't fun.
Regarding your second question, there is something to be said about the composition of a hand. The fewer the decks the more this is true. My blackjack appendix 3A and appendix 3B show the exceptions to single- and double-deck blackjack, based on the composition of the hand. These appendices show that the more cards that are in your hand the more inclined you should be to stand. Regarding your 15 against a 10 example, there are two situations in single deck blackjack where you should stand when the 15 is composed of 5 cards, A+A+A+6+6 and A+A+3+5+5. Note that in both of these situations either two fives or two sixes have left the deck which are the two most helpful cards for the player. The two situations where you should be the most inclined to stand if you have a multiple card hand are 16 against a 10 and a 12 against a 3.

Odds Of Losing 10 Blackjack Hands In A Row

I have said numerous times that there is no long-term way to beat a game with a house edge. If there were a true 50/50 game with no house edge it would be impossible to guarantee beating or losing to it under real world conditions. The results always approach the house edge in the long-term. It is not just computer simulations that back this up but the fundamental laws of probability.
About video blackjack, that may be the way of the future. I have seen fully electronic tables with video display at the World Gaming Expo. I have also seen tables that with cameras can track every bet and every play each player makes. This enables the house to accurately comp players and alert them to card counters. These tables look and feel like any other blackjack table, so you card counters may be out of business if these tables are successful.

I’m not familiar with it. Ken Fuchs co-wrote Knock-Out Blackjack so he can’t be all bad. However I just hear the word progression and I’m immediately skeptical.

Progressive betting systems, like yours, will turn a good session into a great one without the risk of catastrophic loss as with regressive systems like the Martingale. However progressive systems will turn a choppy neutral session into a bad one. Consider what would happen if you alternated between a win and a loss the entire session. The wins would all be at $15 and the losses at $30. Funny you should mention the ’Weakest Link.’ I tried out for that show during the summer and didn’t make it. It is probably just as well because I’m not that witty in real life and doubt I could come up with a good rejoinder to one of Ann’s jabs.

The name for this system is the Martingale. Ignoring ties the probability of a new loss for a hand of blackjack is 52.51%. So the probability of losing 8 in a row is .5251⁸ = 1 in 173.

If you can’t double or split that adds 1.9% to whatever the house edge is otherwise. This just goes to show that you should always have double or split money available if you need it.

That column seemed to put the mathematics to that 'feeling' a player can get. In that columns’ example of a player losing 8 consecutive hands of blackjack the odds were (.5251^8 or about 1 in 173). My question though is what does that really mean? Is it that when I sit down at the table, 1 out of my next 173 playing sessions I can expect to have an 8 hand losing streak? Or does it mean that on any given loss it is a 1 in 173 chance that it was the first of 8 losses coming my way?

I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. I’m still curious though. Besides every once in awhile throwing down a bigger bet just adds to the excitement and for some reason it seems logical that if you have lost a string of hands you are 'due' for a win.

I have no problem with increasing your bet when you get a lucky feeling. What is important is that you play your cards right. Unless you are counting cards you have the free will to bet as much as you want. As I always say all betting systems are equally worthless so flying by the seat of your pants is just as good as flat betting over the long term. When I said the probability of losing 8 hands in a row is 1 in 173 I meant that starting with the next hand the probability of losing 8 in a row is 1 in 173. The chances of 8 losses in a row over a session are greater the longer the session. I hope this answers your question.

Thanks for the kind words. I appreciate the thought of visiting the advertisers. However the casinos don’t care about click throughs as much as they used to and now what matters is new real money players, and how profitable those players are. So unless you might actually play there is no pressure any longer to click through the banners.

Blackjack tournaments are not my strong subject. For advice on that I would highly recommend Casino Tournament Strategy by Stanford Wong. Wong says that if you are behind to bet opposite of the leader, small when he bets big, and big when he bets small. If you are in the lead then you should bet with the second highest player. The book gets into much more detail. Speaking of supporting my site, it helps to click through my Amazon links when buying books there.

Your expected loss of this play is 0.005*20*$1000=$100. The betting system will not affect the expected loss, but will affect the volatility.

Without knowing anything else, if you lost the last hand in blackjack then it is slightly more likely that more small cards than large just left the deck. This would make the remaining deck more large card rich and thus lower the house edge. However I speculate this is an extremely small effect. Yet it does go to show that if you must use a betting system one that increases the bet after a loss is better than one that increases after a win. I hesitate to put this in writing at all because again the effect is probably very small and I fear system sellers will misquote me and imply I endorse any system, which I DO NOT.

You didn’t say how many rounds there were. However, I would bet $10 in all five hands every hand, or go bust trying. With 1,000 players and a relatively low max bet you’ll need all the variance you can get.

I’ve been wondering this myself for years. In 2004 somebody accepted my betting system challenge, claiming he could beat blackjack without counting. The details are in my page on the Daniel Rainsong challenge. After I posted it, I received a message from a blackjack genius, who goes by the handle 'Cacarulo.' He challenged me under the same conditions and blackjack rules set forth in the Rainsong challenge.

Knowing how knowledgeable he is about blackjack, I felt that he was probably right, so I declined the challenge. I asked anyway how he would have gone about his strategy, but he wouldn’t tell me. I tend to think that he would have bet the minimum most of the time, except if it was late in the shoe, and the ratio of losses to wins was very high since the last shuffle, he would have bet the maximum. The reason is that losing is positively correlated to small cards being played, and winning to large cards. In other words, a benefit of losing is that it tends to make the count better. However, this is a weak correlation. My challenge allowed the player a bet range of 1 to 1,000, which is probably enough to overcome the house edge, but it will be hard to find a real casino okay with a jump in bet size by a factor of 1,000.

Odds Of Winning 3 Blackjack Hands In A Row

The short answer to your question is, no, tracking wins and losses will not help enough to warrant the bother of doing it.