Deal or No Deal

Anyone watching this show? What are your thoughts?

What happened to the African American Female in the second half of Monday’s show ?

She failed statistics. She was offered a high of \$139,000, turned it down and picked the highest remainung case at \$500,000. Thanks knocked the next offer down to like 7 grand. Finally there were two cases left. She took the 25,000 offer. It was the right choice, as she had the 75 dollar case.

I wan’t turn it on again tonight, not any way for the audience to really play along.

It was interesting, but I think they should have an audience of Game Theory and Statistics majors instead of the average American idiot.

Play the game free here.
Deal or No Deal

I won \$138,000 and found out I had the \$5 case.

The first couple of times I took the bank’s offer of \$39 grand and \$138 grand. Both times I had the \$1 million case. The third time I stuck it out and won \$500,000.

I wonder if that online version uses the same “offer calculation” as on the show? It doesn’t seem to be a straight return probability calculation (I think that’s what it’s called, where you sum up the reward times the probability of each option), especially if the \$1 million stays on the board for a while.

I caved to an offer of \$291,250 (the \$750k choice stayed on the board until the very end), it turned out I had the \$50k case.

This is the problem I had with it, I will supply it as people have replied.

There is no main point to the show. It is strictly chance. One could even advance the argument that its not a “Game”. No Questions. Its basically two steps above some Las Vegas slot machine.

I want to play for real!! The first time I took 53 grand (highest offer) when the odds turned against me and had the \$100 case. The second time I took \$305,050 with three cases left (\$10, \$75 and \$1,000,000). I had the \$10 case.

And, yeah, this is pretty mindless entertainment.

I got bored with it when there were 3 cases left and went to make a cup of tea. It’s a statistics game based mainly on pure luck and varying levels of cupidity and stupidity. It’s basically an elaborate version of “Let’s Make a Deal” without the fun.

It’s the most mindless, boring game show I’ve ever seen.

This show is going to get boring very quickly. There is no skill involved (other than juggling statistical odds), no questions and answers.

Not so. It’s a matter of balancing your desire to maximize expected value (EV) with your willingness to accept variance.

If the game were played by billionares, or by the same person repeatedly, then what you say would be true. Since every offer the “banker” makes will be below the expected value of eliminating every remaining case but one, you should simply pick a case at random and discard all others. In the long run, this will yield the best result.

What makes it interesting, of course, is that the contestants presumably need the money to one degree or another, and they only get one shot. At what point does it become worthwhile to make a -EV decision by accepting the banker’s offer, so that you can assure yourself of a large prize? Since the EV of the offers becomes less negative as the game progresses, I think, all offers should be rejected out of hand until there are, say, 8 cases left. Anything before that would just be giving up too much EV (and I’m broke). From that point on it’s a judgement call, but there should usually be, IMO, an opportunity to go further at a price that’s irrefusable.

That’s results-oriented thinking. It may have been the right choice for her since getting a sure \$25K was more important than getting the right price (\$37, 537.50 if the other case was the \$75,000 case, which I’m guessing it was). But the decision should not be considered right or wrong based on what the particular outcome would have been.
I think the show would be very interesting if they didn’t draaaaaag . . . . . . out . . . . . . . . . . . . . . . each . . . . . . . deciiiiiiiisssssiiiiiioooon.

This show has been running for some years here. It is generating great free data for economists. I know of two economists at my institution who are using the show.

That occurred to me. “Deal or No Deal” is essentially an extended form of the Monty Haul problem, so the same (or similar) reasoning and strategy should apply.

Drawing on my game theory knowledge, this game is identical to the prizes being generated randomly when each case is selected. Going through the cases in numerical order is strategically identical, I think, to picking them randomly.

Pretty much agreed. Watched the show once and thought it was mildly entertaining. Would I watch it again? Probably not. It’s going to be the same thing over and over.

I watched most of the first show and bits of the second. Doesn’t it seem like there are more commercials than normal? Maybe it’s because they string out every decision, then go to commercial. But it seems to me you could do the show in 30 minutes by not trying so hard to build tension every damn second.

Nope, the other case was \$50,000, so the \$25,000 offer was basically right on. A previous offer that she rejected was even above her expected value for the game: she was offered \$139,000 when there was just over \$550,000 left in 4 cases.

I’ve watched a couple of episodes now. It’s interesting, but certainly not going to have any staying power. I thought it was only going to air for a week or two then go away?

The bankers offers are simply an average. It’s funny that they try to make so much of a big deal about the phone calls and “statistics” and “odds” that go into this decision.

Here’s my take on strategy for the show. You should always take the deal if there are more high cash amounts on the board than low ones. If there are more high numbers that you don’t want to pick then the odds are against you. If there are a large number of lower numbers than the odds are for you. Keep picking until you get the ratio right and then take the deal.

Of couse, as someone already pointed out the best odds, strictly speaking, are to simply take whatever is in your case. But, this leaves you with a great chance at getting next to nothing. I’d rather play a game where I’ve got a solid chance at 100-200K than a slim shot at a million.

The dummy from MA last night had four cases left, IIRC. One was low, less than \$100. The other three were for something like \$200K, \$300K, \$400K each. His friends on the couch even pointed out to him that the odds were against him at this point. He still refused the offer. Of course, his next pick was a 75% of being bad, and it was. In a situation like that you should always take the offer. I think the show deliberately must get morons who can’t figure statistics. They don’t seem to have any clue about playing a strategy at all.

Just over \$550,000 / 4 = \$139,000. There’s no fancy math here. The banker always just offers the expected value for the game. It’s a simple average.

The only thing that makes it slightly complicated is that there are more lower amounts than high amounts. A single high amount will drive the average up, but the chances of getting it are slim. The goal is to keep getting rid of cases until you can get a favorable ratio of large to small amounts. Then take the deal.

Here are the cash amounts:

.01
1
5
10
25
50
75
100
200
300
400
500
750
1000
5000
10000
25000
50000
75000
100000
200000
300000
400000
500000
750000
1000000

So, total of the cash amounts is \$3,418,416.01 and that makes the expected return of just taking your case at \$131,477.54.

Anything above \$131,477.54 means to effectively beat the odds. I’d still turn down an offer above this amount, though, if the remaining cases had the right ratio.

[QUOTE=Scuba_Ben]
That occurred to me. “Deal or No Deal” is essentially an extended form of the Monty Haul problem, so the same (or similar) reasoning and strategy should apply.
QUOTE]

That was my first thought also. But since I only saw about 10 minutes worth, I need to a) watch a little more and b) think about it.

The gist of the Monty Hall problem was that no matter how many doors you open (cases in this case) your odds of having chosen the \$1m case do not change. So here, it would still be 1 in 26. I guess the wrinkle is in trying to weigh in the probability of all the remaining cases.

Also, on first glance it did not seem that the banker’s offers were a straight expected value. Maybe they are varying it for entertainment or research purposes.

There is a very significant differenc in that in the Mony Hall problem, Mony is the one opening the doors and he KNOWS which door has the prize and that is why your odds of having originally picked the right door do not change. In this case, the contestant “opens the doors” so to speak and doesn’t know what is what. So, the odds of having chosen the \$1 mil go up every time a case that is not \$1 mil is revealed.