Optimal Strategy for "Deal or No Deal?"

[monroe]

Here is a taste of what the banker's offers can be like. This is from the end of a recent episode I caught with pencil and paper nearby.

There were five cases remaining: 10, 25, 100, 500000, 750000. The banker offered 199000 (80% of the avg. value, 250000).

The $10 case was opened, leaving: 25, 100, 500000, 750000. The banker offered 279000 (90% of the avg. value, 312500).

The $100 case was opened, leaving 25, 500000, 750000. The banker offered 359000 (86% of the avg. value, 417000). The contestant was informed that this was the highest offer made by the banker in the history of the show.

The contestant accepted the offer of 359000 (on the advice of special guest Donald Trump, shamelessly promoting the new season of The Apprentice). It was then shown that the contestant would have won only $25 had he gone all the way.

[Double Down]

[ QUOTE ]
Usually the Bank will offer significantly less than the average of the remaining cases. Please note, there is a pretty good chance that the bank actually knows how much is in your case, and is making offers using that information. Does this change your EV calculations at all?

[/ QUOTE ]

Actually, I don't think that the banker knows. They state at the beginning of the game that no one knows except for 1 person who isn't the banker. But I do wonder...
Also, for the times when someone from the previous episode continues the next day, I wonder about whether or not they switch the amounts in the cases overnight. Would be a pretty huge scandal, but it would be damn hard to prove. Hmm...

[Annorax]

[ QUOTE ]
[ QUOTE ]
Usually the Bank will offer significantly less than the average of the remaining cases. Please note, there is a pretty good chance that the bank actually knows how much is in your case, and is making offers using that information. Does this change your EV calculations at all?

[/ QUOTE ]

Actually, I don't think that the banker knows. They state at the beginning of the game that no one knows except for 1 person who isn't the banker. But I do wonder...
Also, for the times when someone from the previous episode continues the next day, I wonder about whether or not they switch the amounts in the cases overnight. Would be a pretty huge scandal, but it would be damn hard to prove. Hmm...

[/ QUOTE ]

It's especially hard to prove when you factor in game show SOP of taping four or five episodes a day.

[EJXD2]

Double Down: Although we see episodes on different days, they likely tape all five shows from a week at once. There's wardrobe changes and such, but what we view as a carryover is probably taped the same day.

[Nottom]

From an EV standpoint all the offers are bad. But I'm certainly willing to accept $400K if I was down to $1 Mil and $1 as my only suitcases.

Basically I'd start considering accepting the offer when it gets within 80% of my true EV and is > 100K.

[Easy E]

[ QUOTE ]
The $100 case was opened, leaving 25, 500000, 750000. The banker offered 359000 (86% of the avg. value, 417000). The contestant was informed that this was the highest offer made by the banker in the history of the show.

The contestant accepted the offer of 359000 (on the advice of special guest Donald Trump, shamelessly promoting the new season of The Apprentice). It was then shown that the contestant would have won only $25 had he gone all the way.

[/ QUOTE ]


Average offer $375K when down to two suitcases

625,000 *.9 = 562,500

375,000 *.9 = 337,500

250,000 * .9 = 225,000



If I calculate correctly, the contestant cost themselves $16K by taking the offer without knowing the $25 was in their hand.

Knowing the results, he made $78,000.


The one time I watched this show, I thought I'd calculated the offer price at almost equal to the EV of choosing. Is it possible that the show knows the amount in each case and makes offers accordingly? Another poster already asked this question.

[monroe]

There is an OOT thread which says that when it gets down to two cases the offer made is exactly the average of the two remaining cases. So, Hero's average offer for the final two would have been $416667. He cost himself $57667 by dealing.

Given that we know (in hindsight) what was in his case, he made $46500 (the average offer for the final two would have been $312500).

Note that when only two cases remain, the contestant is given the option of switching cases, just for the fun of it.

As far as The Powers That Be knowing what is in the case, supposedly only one staff member knows what is in the chosen case as the game is going on, and the "Banker" does NOT have this knowledge.

Also, the offers are usually well below average early on, but get closer to the average as the game goes on (although it can bounce around, like in the endgame I wrote about). According to the OOT thread, they recently made an offer that was ABOVE average (but only by $300). The contestant declined the deal.

[Double Down]

[ QUOTE ]
Double Down: Although we see episodes on different days, they likely tape all five shows from a week at once. There's wardrobe changes and such, but what we view as a carryover is probably taped the same day.

[/ QUOTE ]

I'm aware of this. The only reason why I thought that maybe they don't do it in this case is that the audience is very different each day. On Tuesday's episode, the contestant had about 80 people in the audience there to see her, and they weren't there the following day.

[monroe]

I just finished watching tonight's episode. Here is one contestant's journey. The first number is cases remaining, the second is the offer made by the banker, the third is the actual average value, and the fourth is the percentage of the actual average that the banker offered.

20, 32000, 283374, 11%
15, 21000, 161138, 13%
11, 44000, 128734, 34%
8, 92000, 167634, 55%
6, 73000, 140012, 52%
5, 9000, 18015, 50%
4, 23000, 22506, 102%
3, 28000, 28341, 99%
2, 5000, 5012, 100%

The player took the $5000 deal. His case had $25.

The final four cases contained 25, 5000, 10000, and 75000. The banker made an offer of 23000. The average value of the remaining cases was 22506. If the $23000 meant something to him, this was the time to deal.

[Jimbo]

[ QUOTE ]
Actually, I don't think that the banker knows. They state at the beginning of the game that no one knows except for 1 person who isn't the banker. But I do wonder...


[/ QUOTE ]

I don't recall this ever being stated. My understanding is that no one knows which cases are which. After all think about it for a moment. All you need to do is put the money placards in 26 identical cases, mix them up then slap on the numbers on the outside afterwards, it is not brain surgery.

Jimbo