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Most Blackjack Players Don't Understand the Odds

14 July 2003

By Fred Renzey

Today I want to give an illustration of how most people shoot themselves in the foot by misinterpreting the odds while playing blackjack. Suppose you walk up to a table where the dealer has just finished shuffling her six decks. You take a seat at third base and put a bet up on each of two spots. You're fully aware that a six-deck shoe contains 96 tens out of 312 cards, but you have no idea exactly where those 96 tens lie. Now the first round of cards is dealt to four other players besides yourself.

Let's say everybody is dealt a bunch of small cards and the dealer has a deuce up. Suppose further that each player before you takes one hit and catches yet another small card. Now it's your turn. Your first hand is 8/4 and your second hand is 8/3. Seventeen cards have been exposed and not a single ten has been seen yet. The question is, how should you play your hands?

Should you simply follow basic strategy and hit your 12, then double with your 11 -- or should you save the impending ten for your 11 by just standing on your 12?

You realize that the appearance of a ten is growing imminently likely, but here's the key question. Which card is more likely to be a ten -- the next card in the shoe, or the one after it? This is where the majority of players misunderstand the laws of probability, and consequently misplay their hands. The correct answer goes like this.

When the shuffled cards first went into the shoe, 30% of them were tens. Since nobody knew their order, every next card had a 30% chance of being a ten. Now, after seventeen straight non-tens were dealt, 32% of the remaining cards are tens. But again, since their order is unknown, every next card now simply has a 32% chance to be a ten. As hard as it may be to accept, the next card is absolutely no more likely to be a ten than the one after it -- or any other for that matter!

For those of you who are not buying this, let me phrase it another way. Suppose that just before you decided how to play your two hands, the dealer reached into the shoe and reversed the order of the next two cards. Which card is more likely to be the ten now? Remember, the cards were shuffled into an unknown order before, and all that's happening is that they're being shuffled just a tad more now.

Now, I know what most of you are thinking. You're saying, "C'mon, a ten has got to be coming. I mean, what are the odds of dealing 18 cards in a row with no tens?"

Well, I'll tell you what those odds are. They're 942-to-1 against, but that's before you deal the first card. Do you know what the odds are after you've already seen the first seventeen non-tens? They're a little over 2-to-1 in favor of the eighteenth non-ten! That's right -- and it's all because only 32% of the remaining shuffled cards are tens.

Let me try to get you to see this concept with one more common example--this one from the game draw poker. What do you suppose your odds are of being dealt a flush on your first five cards? They're 504-to-1 against. But suppose that after looking at your first four cards, they're all spades. What are your chances of being dealt a flush now? They're just a little more than 4-to-1 against! Why? Because you've already got the first four parts. Being dealt a pat flush before any cards are dealt and getting that flush after you're already holding a four-flush are two completely different things! Likewise, dealing eighteen straight non-tens in blackjack before the first card is dealt is a huge longshot, but if you've already seen the first seventeen--it's actually likely!

So remember, when you see a string of high or low cards come out at the blackjack table, don't misplay your hand by assuming that the next card is more likely to be a certain type than the one after it. As long as there are at least two cards left, this is never true!

Fred Renzey
Fred Renzey is a high-stakes, expert poker player. On a daily basis he faces--and beats--some of the best players in the country in fierce poker room competition. Now for the first time, Renzey offers his perceptive insights on how to play winning poker. For Fred's 13-page blackjack booklet "Ace/10 Front Count", send $9 to Fred Renzey, P.O. Box 598, Elk Grove Village, IL, 60009

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