The Math Proves That Bad Blackjack Players Don't Hurt You

The most common complaint I get from blackjack players is that they lose because other people at the table play their hands wrong. But the reality is, if you've been unable to win -- it's been all you!

Blackjack experts realize it doesn't matter how anybody else plays his hands. All that matters to you is how you play yours. Yet, most regular players just don't buy it.

Fact is, it can be mathematically proven that another's play has no effect on your own chances to win. In its pure form, this proof is an algebraic expression. But here, we'll convert it into a story problem that you should be able to solve for yourself.

Suppose you're sitting at first base and there's just one other player at third. Here are everybody's hands:

You make the proper play and stand. Now it's third base's turn. You don't really care whether third base wins or loses -- you just want to win your own hand. So I'm going to ask you this next question three times.

Which way are you more likely to win your own hand – if third base stands or hits?

Most players would want third base to play it "by the book" and stand. They fear if he plays it wrong and hits, it'll probably cause the dealer to make a good hand. Is there some reason why this should be true? Without thinking it through, it's hard to answer logically. So let's go a little deeper to help us understand better. Suppose the dealer flashes you her hole card and she has:

6 / 10

She's definitely got 16. Furthermore, we'll say there are only five cards left in the shoe and they are:

J – Q – 5 – K - 10

Four of the five remaining cards are 10s. Still, though, there's one little problem. Those five cards were scrambled, then stacked in the shoe in an unknown order. That one lone 5 could be next, last, or anywhere in between.

So I'll ask you for the second time. How do you want third base to play his hand? Let's analyze it.

If third base stands, we can see that the dealer will break four times out of five. But how often will the dealer break if third base hits? Here's where the mathematical proof comes in. Follow it closely.

On four hits out of five, third base will take a 10. Those four times that he catches a 10, there will be four cards left for the dealer and three of them will be a 10. So the dealer will break three out of those four times. But third base's fifth hit will be the 5. That one time, the dealer must break since nothing's left but 10s. So it turns out that the dealer still breaks four out of five times whether third base stands or hits.

Now I have to ask you one last time. How do you want third base to play his hand? When you can say, "I couldn't care less", you've expelled some major demons from your game.

Now I know you'll never be playing with a shoe that has only five cards in it. Understand, however, that it doesn't matter whether the shoe contains five cards, fifty cards or 200. If you run through all the possible scenarios for each set of remaining cards, you'll still find that the dealer will break the same number of times whether third base hits or stands.