“Dill, or no dill?” was the question asked of my colleague/friend by the counterperson as she was finishing his sandwich at a local casino’s snack bar.  This was shortly after “Deal or No Deal” became popular.

If you’re like me, a nerd with time on his hands, you watch some game shows now and then.  At first blush, Deal or No Deal seems to be trash TV, especially as compared with Jeopardy - but is it really?

At any point in the game, you can add the prizes on the board and divide by how many there are to get the Expected Value (EV).  EV is a technical term in gambling (from probability and statistics) - see for example http://en.wikipedia.org/wiki/Expected_value.  If you could play the game forever with that same board, the earnings per game would approach the EV as the number of trials increases.

I have never seen a banker offer equal to the EV.  For most of the game it is less than the EV, but very late in the game it may exceed the EV.

If you could play the game as many times as you wanted, then you should seemingly decide to take a deal based on the EV.  Generally you would refuse banker offers and play on, since they tend to be meager most of the time.  If you read the preceding sentence and think, “No, I would just take any decent sum and play again, and I would soon have enough money for my lifetime and could get back to playing Angry Birds,” then you are venturing into the realm of the Utility Function. You can find technical definitions of this term (e.g., http://en.wikipedia.org/wiki/Utility), but for my purposes here let’s define it as “enough money to reach some goal I have.”

Frequently game participants speak of something they want money for: pay off their house, have enough for college for the children, have enough to attempt a career change … the list is endless, but the items are familiar.  Yesterday I heard a new one: a woman was playing with her fiancé in attendance, and she wanted to pay off their divorce lawyers - who had helped this same couple divorce!

One can approach this game in myriad ways, but here are three possibilities:

1. maximize EV.  No one does this, and most participants probably couldn’t calculate EV, though they know the early offers are too low: “$20,343 when the board has $1M and several amounts in six figures? I don’t think so!”  They are correct to reject these offers early because (a) EV doesn’t rule when you only have few trials, let alone only one, and (b) the average board value, and thus a banker offer, is likely to be higher at some point than it is at an early stage, although this is not guaranteed.

2. satisfy their personal utility function:  If you need $150k to pay off your house, you take any offer near that unless you seem to have an overwhelming chance of going higher by playing on.

3. greed.  Most people seem to get caught up in playing the game, and the prospect of winning more money overtake their more sober instincts.

The woman about to remarry her former spouse was a prime example of #3.  The board was salted initially with 8 $1M entries.  When I started watching there were 4 of these 7-figure Sirens (http://en.wikipedia.org/wiki/Siren) remaining.  Slowly they were trimmed away, but the offers mostly went up.  As the game ground onward, she knocked all but one $1M off the board, and when this penultimate one was removed, the bank offer went down.  She rejected it and played on, and had a favorable round.  The bank offer went to six figures for the first time, and the board now contained 3 small amounts, plus $1M.  Her response was NO DEAL!!!! Sadly, on the next round she selected the last $1M case, and the divorce lawyers wound up having to wait for their money.

What causes people to abandon their game plan and play on?  Greed? Intermittent reinforcement?  Too many bright lights and people shouting No Deal?

I sympathize.  I’m a more disciplined gambler than most, but I have found myself playing for One More Positive Fluctuation when my goal for that casino on that day was already achieved.  I got caught up in the game.

I wonder, though, about these people and the irrational risks they take sometimes.  Do they have some unstated financial guarantee for playing on, like poker tournament players who agree to a split, yet play on at the final table for the cameras?  Is that even legal now in U.S. game shows?  I wonder.

Another observation: suppose the board contains $1M, $100, $10, and $1.  The bank offer is $200k.  To play on, one must open one more case.  If it contains the $1M, then the player has effectively lost $200k. If it contains a small amount, the next offer might be $275k. Thus the player should have accepted the $200k offer unless that sum is worthless to them, while $275k would satisfy their goal.  In rejecting the $200k offer, they seem to be behaving as though they are going to get the $1M in the next round!

To digress a bit, what explains the Stepford contestants on so many shows, such as Wheel Of Fortune and Family Feud, who furiously applaud even when the game goes against them and in favor of their opponents?  I would have to be bleeped and my mouth image pixelatted.  What drugs do they give these people?

Addendum:

Since there are so few large amounts on the game board, the median might be a better measure of short term expectation.  See http://www.statisticsmentor.com/topics/dond.htm, which offers a nice summary of the basics.

A succinct analysis from a game theoretic perspective may be found at http://en.wikibooks.org/wiki/Introduction_to_Game_Theory/Deal_Or_No_Deal.

Still pounding in some nails, trying to get the walls to stay up, but here’s a first post anyway.  I need to find a picture too.

You’d think I’d have used the “redux” theme for this blog, but it appears to be the all-too-commonly-used default here on tumblr.

Things to know about me that are relevant to my quest:

- I retired way early, 10 years ago from compiler development at a big software/hardware firm.

- Since my retirement, I’ve been gambling for a living, but things are getting tougher in my preferred activity as the casinos wise up and learn how to mine their data.  I haven’t been affected much yet, but that could change.

- I’m trying to figure out what to learn to make myself employable doing something I’d enjoy.  Simply refresh myself on C/C++?  Learn Java?  Figure out what’s up with PHP/Python/Ruby/RubyOnRails/Scala/whatever?  Apparently something called the World Wide Web has just about taken over the universe of s/w development while I was busy trying to win money and beat Bejewelled/Chuzzle/AngryBirds.  The landscape has changed, and now when people talk about high level languages, my adopted tongue C++ is often not mentioned at all.  Wha????

- I’ve downloaded all three of the intro CS courses offered by Stanford Engineering Everywhere, and I plan to start them in late October, and finish them all by mid-December.  These should help me get my head back into writing code.  Apparently I’ll be learning some Java … 

- Because of my age, I’m thinking of seeing a career coach for tips on how to finesse that issue during the hiring process.

Here’s my current manifesto, or part of it at any rate.  The specifics are valuable, the path is walkable, but I also like the mantra: No One Can Stop You.  Check it out: http://495west.com/post/9885249988/the-wrong-question-i-want-to-learn-to-code-what

Coming soon: how I got interested in getting back into it, apart from needing money 8-).

Comments are more than welcome.  I gotta figure out how to put up an Ask button or some such.  No one can stop me 8-).  Cheers ….