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Best of Fred Renzey

Gaming Guru

 

The Odds Aren't Always What They Seem

24 April 2004

Most serious gamblers are rather proud of their understanding of the odds and how they work. Still, it's easy to misjudge their true properties and get those odds all messed up. That's why so many ardent gamblers repeatedly reason against the odds. Want a cute example of how the real odds can trick you? Use this one to fool and impress your gambling cronies.

Take three cards out of the deck -- two Jacks and an Ace. Turn them face down, scramble them and have your buddy try to pick out the Ace, but don't let him turn his card up yet. Have him just keep his hand on top of it.

Now you go ahead and peek privately at the other two unchosen cards. There will always be either one or two Jacks. In either case, always go ahead and turn one Jack face up and push it right out of the picture. That will leave just two remaining cards in contention -- your friend's pick and the orphan card. Obviously, one of them must be the Ace.

Here's the coup. Before your friend turns his card up, ask him whether he likes his pick and wants to stick with it, or if he'd rather switch to the other card.

Most gamblers will say that since there are only two cards left, it's even money and makes no difference -- but they're wrong! Actually, your friend is a 2-to-1 underdog to have the Ace, and the orphan card is a 2-to-1 favorite!

If your friend insists his chances are 50-50, that's where the fun begins. Lay him odds, say 3-to-2 that he's holding a loser. You'll have an 11% edge on the price you're laying. Why?

At the moment your friend picked out his card from the three, he was a 2-to-1 dog to choose the Ace. Whether he succeeded or not, you can always find a Jack to turn up among the other two cards. And after you do, he's still holding the same card. Nothing has changed!

I know what you're thinking. You're saying, "Wait a minute! There are two cards left, and since one of them must be the Ace, each card has to be a 50% shot. After all, the two cards together have to add up to 100%."

Well, they do add up to 100% -- but they're not each 50-50. The card your friend chose was -- and still is -- a 33% shot, but the orphan card is a 67% shot! Two times out of three, the orphan card will be the Ace! Therefore, your friend should always switch cards. Don't take my word for it. Play the game out 40 or 50 times and you'll see.

Okay, so what does all this have to do with casino games? It merely shows that you need to focus on the big picture when you're gambling. Don't read meaning into things that change nothing. Take the classic case where you're at first base with 13 against the dealer's 6 in blackjack. If you knew the dealer had 16 and there were only three cards left in the shoe -- two 10s and a 5, would you want 3rd Base to hit or stand with his stiff?

Most gamblers will reason that if 3rd Base hits, he'll probably take a 10 and that'll increase the dealer's chance to make a hand. Well, that's exactly true -- for what's been said so far. But there's more.

What happens if 3rd Base takes the 5? Now the dealer will positively bust. The thing of it is, those two probabilities will always cancel each other out perfectly -- no matter how many cards are left or how many of them are 10s. Let's prove out this particular example.

Two out of three cards are 10s. If 3rd Base stands, the dealer simply breaks two out of three times and that's how often 1st Base wins the hand.

If 3rd Base hits, he takes a 10 two out of three times and the dealer breaks half of those two times (since that leaves one 10 and one 5). The third time, 3rd Base takes the 5 and the dealer positively breaks. So again, the dealer ends up breaking two out of three times that 3rd Base hits. Again, nothing has changed!

Now go ahead and change around the remaining supply of cards any way you like and you'll find that the dealer's break percentages with 3rd Base hitting vs. standing will always match. Take that to the bank.

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

Books by Fred Renzey:

Blackjack Bluebook II

> More Books By Fred Renzey

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

Books by Fred Renzey:

> More Books By Fred Renzey