The Difficult Task of Killing a Bad Idea.
by Ash Bishop
There’s a moment in Alan Moore and David Lloyd’s 1982 series V for Vendetta when the central character, named V, is fatally shot by the police. He’s alone, in a dank sewer system and it seems his crusade is over. Instead of admitting defeat, he makes a stirring declaration: “Did you think to kill me? There’s no flesh or blood within this cloak to kill. There’s only an idea. Ideas are bulletproof!”
V is a madman, but the good kind. He hides beneath a mask and a wide-brimmed hat in order to fight against a Totalitarian government. He’s inspired by the ideas of another British revolutionary, Guy Fawkes, and he literally wears Fawkes’ face – another nod to the undying power of an idea.
The problem is, what do you do when the idea is a bad one, and it still won’t die? The best example of this conundrum is, of course, racism. A race gains a reputation for having a specific, negative quality and that evil expectation sends damaging psychic runoff outward in endless waves.
I could write a hundred blog posts on the fallacy of racism, or the dangers of Totalitarianism, or how our individual consciousness is at the nexus point between inductive and deductive reasoning — and that’s what makes life so dang confusing. And maybe someday I will. But I want to start a little bit smaller. Today, I want to talk about Blackjack.
Let’s talk about one of the ideas that has raised ornate, gilded casinos from dust out there in the vast desert.
Before I go any further, how about a disclaimer? I’m an English major with a master’s in CREATIVE WRITING!!! I haven’t consulted a mathematician in any way in writing this. Everything I say from this point on should be wholly ignored.
Seriously, pay attention to that warning.
Anyway, here’s the situation. You sit down at a table at Circus Circus. Because it’s inevitable, the dealer deals you a sixteen. Because it’s also inevitable, the dealer deals herself something higher. In this case, let’s say a seven. Her other card is turned down – you have no idea what it is.
You hesitate, trying to run the probability in your head, and that’s when the final inevitability occurs. The big fella next to you leans over and points at the dealer’s seven. “She’s showing seventeen,” he says. “You have to assume that the hole card is a ten. You need to take another card or she’s going to beat you.” The big fella is smug, but he’s also happy to help. It’s fun for him to see that you don’t understand blackjack’s simplest rule.
He is also, of course, dead wrong. Let’s address the obvious first. If you are to assume that every card is likely to be a 10, that means the card he’s encouraging you to draw from the deck will also be a 10, putting you at the lovely total of 26.
That said, the real math is pretty simple, but not in the way the helpful big fella believes. See, there are thirteen different cards in the deck, divided equally in sets of four: 2-3-4-5-6-7-8-9-10-J-Q-K-A. Casinos tend to use multiple decks, but the percentage change is small enough let’s ignore that for now.
Instead, let’s figure out the simple math about the dealer’s hand. She has a seven showing, which means of the thirteen possible draw cards, five of them will help her beat your sixteen (10-J-Q-K-A), while the remaining eight (2-3-4-5-6-7-8-9) will force her to take at least one more card, with each new draw increasing her chances of busting. In other words, she’s only “got you beat” as the big fella likes to say, in 38.5% of potential draws. In the other 61.5% of draws, her situation becomes increasingly more perilous.
Here’s how the math shifts with the dealer showing eight (her winning cards are 9-10-J-Q-K-A; 46.2%), and nine (her winning cards are 8-9-10-J-Q-K-A; 53.8%). With any type of ten, you already know she doesn’t have an ace in the hole because it would have ended the hand immediately. So, her potential winning cards are 7-8-9-10-J-Q-K. That’s still only a 53.8% chance she beats you without having to draw. In all those situations, the odds are hovering around 50% that her hole card helps her, and 50% it’s a card that will require another draw.
Of course, in 100% of the cases, that second draw will be exactly what she needs, because casinos like to give you a little hope before tearing out your heart and stomping on it.
One of the casino’s big advantages is they make you play first. If you bust, they whisk the money right off the table before the dealer even has to test her own odds. So, it’s much more important to consider your own odds while holding that sixteen.
Five cards will help you (2-3-4-5-A; 38.5%), eight cards are waiting to ruin your day (6-7-8-9-10-J-Q-K; 61.5%).
Here are the odds if you’re at 15, five help, 38.5%; seven bust, 53.8%; one makes your hand slightly worse, 7.7%.
In the case of 14, five help, 38.5%; six bust, 46.2%; two make your hand worse, 15.4%.
In the case of 13, five help, 38.5%; five bust 38.5%; three make your hand worse 23.0%.
Notice the pattern? It’s the same thing if you’re holding 12. Your odds of getting a card that will get you above 17 but below 21 never improve from 38.5%. It’s the real reason you “don’t like gambling”.
In regards to “always doubling down on 11”, most casinos only give you one more card on a double down, so the math is a little easier. Eight cards get you to the magic seventeen (6, 7, 8, 9, 10, J, Q, K; 61.5%). That’s as close to “always” as you can get in blackjack. Interestingly, doubling down on 10 doesn’t change the odds at all. There’s still a 61.5% chance you get a card that puts you between seventeen and twenty-one (7, 8, 9, 10, J, Q, K, A). Always double down on ten?
You can also lose at seventeen, by the way. And at eighteen, nineteen and twenty.
If this is making your head spin, consider that it gets even more complicated when you start to factor in multiple draws, which play a part in almost every hand. The inside of your brain ends up looking something like this:
TL;DR section here.
So, what’s a truly simple system like the one the big fella is sharing with you, but without his tragically bad math? Consider your goal is to get between seventeen and twenty-one regardless of what the dealer is showing. Even though those amounts can still lose, they are considered “winning hands” because the dealer will never stop at sixteen and will automatically lose at twenty-two. Remember also that you’ve got to do it safely, or not at all. Here’s the plan:
Double down at ten, and at eleven. If you’re sitting at any of the dreaded 12, 13, 14, 15, 16, try to remember that you never have a better than 38.5% chance of reaching a “winning hand” on a single draw, and increasingly worse odds of busting (30.8%, 38.5%, 46.2%, 53.8%, 61.5%).
I’d play the bust odds and take another card on the 12, 13 and 14 but hitting on fifteen is truly a gamble (you’re giving up 3.8% in favor of busting with another 7.7% you draw an ace and holding your position), and hitting on 16 is, mathematically, almost always a mistake, regardless of what the dealer is showing.
Fifteen and sixteen have done their part to build the casinos, assisted by the complicated nature of multiple draws as well as the incredibly powerful force of irony. As you know, irony is an immutable, physical law of the universe that determines that you will always lose, no matter what.
Bad ideas, and the subsequent social pressure that accompany them, are almost as frustrating.
Let’s go back to the table at Circus Circus where you have sixteen and the dealer is showing a seven. You sit at sixteen because that’s what the math says. The dealer goes next, and because of the power of the aforementioned irony, she turns over a ten and then draws a four, putting her at twenty-one.
The big fella’s congeniality crumbles. He is confident in his own lousy math, and worse yet, he thinks there’s a divine order of cards. You messed it up by not hitting and stole his “win.” His face turns sour as the dealer grabs his chips, and he mumbles “Folks don’t even know how to play the game.” He sips his Heineken and refuses to look at you.
You want to tell him about the math behind fifteen and sixteen. You want to explain that there’s no actual divine order. You didn’t make him lose! Every draw is random chance, and there’s a one-in-thirteen probability of getting any card every single time one comes out of the shoe. This is true regardless of what the person before you decided, or what the person after you decides. It’s not your fault! It’s not! If it weren’t for the interminable power of irony, the dealer had just as good odds of drawing a five and busting. Or a six.
Wait… that’s not exactly true. Four of those thirteen cards have the value of ten. So…you know…it’s safe to assume that every card is a ten. It’s four times as likely as anything else!