Ask The Wizard #150

Deal or No Deal just started here in the U.S.. The rules sound the same except our prizes go up to a million dollars as follows.

1. 0.01
2. 1
3. 5
4. 10
5. 25
6. 50
7. 75
8. 100
9. 200
10. 300
11. 400
12. 500
13. 750
14. 1000
15. 5000
16. 10000
17. 25000
18. 50000
19. 75000
20. 100000
21. 200000
22. 300000
23. 400000
24. 500000
25. 750000
26. 1000000

Here is the flow of the game:

1. Player picks one case for himself
2. Player opens up six of the remaining 25 cases.
3. Banker makes an offer.
4. If player declines he opens five more of the 19 remaining cases.
5. Banker makes an offer.
6. If player declines he opens four more of the 14 remaining cases.
7. Banker makes an offer.
8. If player declines he opens three more of the 10 remaining cases.
9. Banker makes an offer.
10. If player declines he opens two more of the 7 remaining cases.
11. Banker makes an offer.
12. If player declines he opens one more of the remaining cases.
13. Keep repeating steps 11 and 12 until player accepts an offer or player has the last unopened case.

I have watched three games in their entirety. The following table shows the remaining prizes, average amount, and banker offer of what I will call "game 1."

The following chart plots the player’s expected value and the banker’s offer.

Next are the same table and charts for games 2 and 3.

The most obvious thing to be learned from these three charts are that the first four to six bank offers are terrible deals. The average suitcase has $131,477.54 before any are opened. To only offer $9000 to $13000 the first stage is a deal only a fool would make. However gradually the offers get better. Game 2 shows us the expected values were almost the same as the banker offers towards the end of the game when the player’s expected value was fairly low. However in games 1 and 3 when the expected values were higher the banker apparently was trying to take advantage of the risk averse nature of most people when large amounts are involved. I don’t know if it mattered but the contestant in game 2 appeared to be a gambler who wanted to win big. Based on comments by the host, who communicates to the banker by phone, the banker does appear to take the contestants words and actions into consideration. If I were in the banker’s shoes I would act much the same.

If the player is neither risk averse nor risk prone, and also ignoring tax implications, the player should keep refusing banker offers until one exceeds the average of the remaining suitcases. For most people the progressive nature of the income tax code favors taking a deal. As I have said before I would roughly say the value of money is proportional to the log of the amount. So the more wealth you have going into the game the more inclined you should be to gamble and refuse the banker offers. With such large amounts involved, no strategy will fit everybody. However I can fairly confidently say that the player should refuse the first four to six offers and then take the offers on a case by case basis (pun intended).

Links:
You can watch Deal or No Deal at NBC.com.
Archive of past shows.

That is a good question. Personally I eyeball the borderline plays based on what has already been played, especially on the second hand to be played. If forced I would say using the exceptions is better than the basic strategy only. However the way the basic strategy exceptions were created was on the initial hand only, so they are not entirely accurate for splitting, because the deck composition will be a little different.

Believe your friends. Often love can cloud one’s judgement, while your friends can see more clearly see what is going on and can give good advice. Lying is also a big strike against this guy. Move on with your life.

Because it is so much fun!

Thanks for the kind words. You are right, if the expected value is less than -1 then you should opt to take the double down surrender. As you said if the expected value for standing in my blackjack appendix 9 is less than -0.5 you should surrender, because you are betting two units. I would only add to your strategy that if the dealer hits a soft 17 then you should also surrender 17 against an ace.

I was recognized in Reno when counting once, although it may have been by dealer who knew me personally and tattled. It is a long and bizarre story. Aside from that I don’t play often, nor for high stakes, so the threat I pose is fairly small and not worth the fuss of memorizing another face.

Under typical Vegas rules (6-deck, dealer hits soft 17) the house edge by always standing is 15.7%. In the short-run one could still overcome that, but in the long run you’ll lose badly.

You can’t fault him for being a nice guy. What I think is unhealthy is your jealousy.Unless don’t stop trying to keep him on a short leash I think a second breakup is inevitable.

Thanks. If your goal is to win just one unit I agree craps is the best place to start. The don’t pass is slightly better than the pass. However if you lose your first bet I would switch to blackjack. Only when exactly where you started would I go back to craps. This is because you won’t need to double or split to win just one unit, and a hit/stand only blackjack game has a house edge of about 2.5%.