Against The Odds

Speaking of game shows, I saw a startling example of bad luck earlier this week on Deal Or No Deal. (If you want to know how it's played, read my earlier post.) What makes it especially painful is how well the contestant was doing before things fell apart.

Here's the situation: She has only five briefcases left with huge money still in play. The amounts are $1, $50,000, $300,000, $500,000 and $1,000,000.

The bank offers her $299,000 to quit. It may seem hard to turn down, but I understand why she doesn't make the deal. If she picks one of the two lowest briefcases, the offer will probably go up to around $400,000. If she picks the middle amount, the offer won't change much. Even if she picks the half million, she'll still probably have an offer over $200,000 and a rich exit. The only disaster, which she can still probably recover from, would be to pick the million dollar briefcase--which, of course, she does.

So the bank drops the offer down to $144,000. This is still a nice chunk of change, but she refuses the deal. Not the worst idea. She's not simply chasing losses. She's got a 50% chance of upping the offer to over $200,000 by picking one of the two smaller amounts. Even if she picks the $300,000, the offer will drop but remain over $100,000. The only disaster would be picking the half million--which, of course, she does.

So the offer drops to $70,000. A nice amount, if you can forget the last two offers. Does she take the deal? No. This is the right percentage play since she's got a two in three chance of improving that offer to $150,000 or more. The only disaster would be to pick the $300,000--which, of course, she does.

Now the offer is a paltry $25,000. (Paltry? I'd happily take it.) Should she stick with her own briefcase or take the offer? It's the old bird in the hand. She figures at 50/50, it's finally time to make a deal. So they open up her briefcase and, sure enough, it's worth $50,000. She made the wrong choice again.

That makes the worst pick four time in a row. What are the odds of this happening? 120 to 1.