Gambling Tips > Blackjack

Will My Money Last?

By Henry Tamburin


I received an unusual question from an 82-year-old blackjack player, whom I’ll call Ed (not his real name). He sent me a letter that said in summary: “I’ve been playing blackjack for 40 years and I enjoy the camaraderie of playing. I’m OK financially, and what I’d like to do is to set aside $75,000 to play blackjack more frequently (four days a week). How long will my money last?”

 

It turns out that Ed was married for 55 years and his spouse recently passed away after a long illness. To combat his loneliness, he started to play blackjack regularly at a local casino. Now he wants to play more frequently to stay “active and mentally alert.”

 

He mentioned in his letter that his local casino offers double-deck ($10 minimum) and six-deck ($5 minimum) games. Ed would like to play “about 3-hour sessions,” and he made it a point to tell me that he “knows his basic playing strategy cold.”

 

If Ed sticks to his plan, he will be playing a lot of blackjack every year: 62,400 hands to be exact. This assumes that he plays 100 hands per hour for three hours on each visit, four days a week for 52 weeks.

 

In Ed’s local casino, the rules specify that the dealer hits soft 17 (h17) in all games, meaning the house edge that he will face is 0.40 percent in the $10 double-deck game and 0.56 percent in the $5 minimum six-deck game. (Note: The exact rules are: h17 and das in the double-deck game, and h17, das, and resplit of aces in the six-deck game.)

 

To answer Ed’s question, I calculated how much of his bankroll would be consumed if he played for 10 years, and also 15 years, and how much (if any) of his bankroll would be left. The results may surprise you.

 

Ten Years
Over the course of 10 years, Ed will play 624,000 hands of blackjack. If he plays solely the double-deck game with $10 minimum bets, here’s what will happen:

 

He will make over 6-million dollars in bets ($6,240,000 to be exact).
His theoretical loss is $24,960 (based on the house edge of 0.40 percent).
His actual loss with 95.4 percent probability will fall in the range of -$6,792 to -$43,128.

 

The above calculations show that Ed has more than enough bankroll to last him 10 years even if he lost $43,128, which is the lower end of the range.  At age 92, he would still have at least $31,872 left of his original $75,000 bankroll. And get this: the chance that Ed would lose more than $43,128 over 10 years is only 2.3 percent (or 1 in 43), giving him even more reassurance that his bankroll will last.

 

Fifteen Years
Here are the results if Ed played the double-deck game for 15 years.

 

He will make $9,360,000 worth of bets.
His theoretical loss is $37,440 (based on the house edge of 0.40 percent).
He has a 95.4 percent probability that his actual loss will fall in the range of -$15,188 to
-$59,692.

 

Even after 15 years of playing, at age 97, Ed’s bankroll will have lasted, and, in fact, he would still probably have at least $15,308 left. (And he has only a slim 2.3 percent chance of losing more than $59,692.)

 

What if Ed decides to play the six-deck game with $5-minimum bets? The table below summarizes the results (along with the results for the double-deck game).

 

The data in the table show that no matter which game Ed plays, as long as he sticks to the basic playing strategy and makes only minimum bets, his $75,000 bankroll is sufficient to allow him to play four days per week with three-hour playing sessions for 10 or 15 years.

 

Game

Years

Worst-Case Loss

Amount of Bankroll Left

Double-Deck ($10)

10

$43,128

$31,872

Double-Deck ($10)

15

$59,692

$15,308

Six-Deck  ($5)

10

$26,556

$48,444

Six-Deck ($5)

15

$37,334

$37,666

 

I sent Ed the above information, and also suggested that he obtain a Player’s Card and always get rated when he plays. I don’t know the specifics of his local casino’s comping policy but, if it’s like most casinos, he will get comps worth about 25 percent of what the casino expects to win from him (and more than likely they will rate him as losing one percent of everything he bets). This means Ed can expect to get roughly $23,400 worth of comps over 15 years of playing the double-deck game (or roughly half as much if he instead plays the six-deck game). The comps are a nice perk that will cover about 40 percent of his loss.

 

I also cautioned Ed to avoid using a betting progression because his average bet will increase, as will the standard deviation (or how much he will stray from his expected loss). This will result in a wider range for his actual loss and a greater worse-case loss over 10 (and 15) years. I also suggested that if he gets the urge to bet more than the minimum, he should do so only when the remaining unplayed cards are richer in tens, picture cards, and aces. (I told him to play the double-deck game, watch the cards that were played, and if he didn’t see many of these cards played after the first two or three rounds after the shuffle, then and only then should he consider to modestly increase his bet.)  (Note: I also summarized for him the pros and cons of learning and using a simple card counting system, but at his age Ed decided for now that he wanted to stick with the basic strategy.)

 

I wished Ed a long and healthy life and “good cards” at the blackjack table. He thanked me for the information and said he felt good knowing that his $75,000 bankroll will “probably last me for the rest of my life.” Ed also promised that he would write and let me know how he was doing. Perhaps I’ll continue the saga of Ed’s blackjack adventure in a future column.