How much do bad blackjack strategies affect good players?

The set-up

I don’t play blackjack very often, because it’s not a very inviting game. Mostly, this has to do with the people playing the game, of course. But for some reason, every table I’ve ever sat at was filled with cranky “experts” interested mostly in telling me how I was ruining their game. In roulette or craps, you just put the money down and people have fun. When I learned to play Pai Gow, the whole table was in on the fun, reveling in successes and kvetching over bad beats. In both cases, it is easy to see how one player’s win or loss is independent of another’s. In both cases, other players are happy to let you play any which way you choose, because they know that no matter what you do, you’re only affecting yourself.

Not so at the blackjack table: in blackjack, players have a choice after the hand is dealt to take more cards from the shoe. It is this fundamental difference, this choice that players make hundreds of times an hour while playing blackjack, that turns the blackjack table into an inhospitable wasteland. And so the obvious question to ask is how large an effect do the other players actually have on your individual success or failure at the table on any given night. And the obvious answer is that of course other players affect my game: they’re taking (or not taking) my cards! But the obvious answer is wrong. Other players don’t actually have that great an influence on your winning or losing. The greatest influence on your winning or losing is, in fact, yourself, and your own luck.

Anyone who has played blackjack for more than a few minutes—anyone who has sat at a table and played and lost 10 hands (like myself)—has heard of basic strategy. Fewer of those people have actually taken the time to memorize basic strategy, of course, because gambling is supposed to be fun and risky; it shouldn’t feel like schoolwork! And yet not using basic strategy is the number one way to increase your losses at the blackjack table.

But let’s answer the question at hand. How do other players affect my expected winnings? In the short run—on any given hand, say—it is quite possible for other players to make you lose. They could take an extra card and get a ten. If the dealer has 16, that 10 would have busted the dealer and you would have won, but instead you lost. And that sucks for you, so you look for someone to blame and it might as well be the person who didn’t use basic strategy, who hit when he should have stood.

But in the long run—over a weekend in Vegas, or over all the hands of blackjack you ever play in a casino—other players don’t matter. Even though there may be six other people at the table, your winning or losing depends more on the strategy that you yourself use, and the luck that you yourself have, than on anything those six other people do.

The simulation

Theoretically, we could probably find the answer to this question analytically. Determine the probabilities of everything that happens in a game, factor in all the choices players make, and see what our formulas spit out. But that would be difficult, to put it mildly. So instead, we enlist our friendly neighborhood Python. I wrote a program that plays Blackjack and, crucially, allows players to use different strategies. Then, I told the program to play 10 million hands of blackjack.

To put that into perspective: if you went to the casino every Friday, Saturday and Sunday and played for 10 hours each day, and managed to play 100 hands every hour… it would still take you 64 years to play 10 million hands. In other words, 10 million hands is more than enough to represent your entire lifetime of play. It probably represents multiple lifetimes of play for the average person, actually.

The two graphs below represent 10 million hands played at each of two tables. On the left, all of the players used perfect basic strategy. On the right, only one player used basic strategy, while the other players used a variety of bad strategies—you can read more about those bad strategies below.

You should notice at this time that the percentages are, basically, the same. At the perfect table, the player using basic strategy lost 46.33% of the time, won 45.67% of the time, and pushed 8% of the time. At the circus table, on the other hand, the player using basic strategy lost… 46.35% of the time, won 45.65% of the time, and pushed 8% of the time. That’s an extra .02% hands lost, or 2,000 hands in 10,000,000. In case you’re having difficulty visualizing the difference between those percentages, here are the two graphs merged:

The details

The simulation used the following rules: dealer stands on soft-17, four decks, double after split, double on any two cards, unlimited resplitting, blackjack pays 3:2.

There were six players at the circus table, using one of four strategies: basic, assume the dealer has a ten hidden, never bust, and play like the dealer. Each of the strategies plays exactly like it sounds. The person assuming the dealer has a ten hidden hits until he busts or his total is higher than the dealer’s shown card plus 10. The person playing never bust strategy always stands if there is the possibility of busting by hitting. The person playing like the dealer stands on soft-17 and hits if his total is less than 17.

All of the strategies that are not basic strategy are very bad. Don’t use them. The important thing is that even though they’re horrendous for the person using them, they don’t affect anybody else in any significant way. Your worst enemy at the blackjack table is yourself, really.

The takeaway

If you don’t know basic strategy, and you want to minimize your losses at the blackjack table, you have to learn it. If you do know basic strategy and you notice someone at the table not using it, take comfort in knowing that they’re only hurting themselves.

And feel free to politely offer to help them learn. Don’t be a jerk about it, because that’s no fun for anybody.