Deal or No Deal: Play the Deal or No Deal online game

Dear Mark,
There is a game show called Deal or No Deal. The participant selects a brief case containing anywhere from 1p to £250,000, and there are 22 cases to choose from. Then, all non-selected cases are slowly revealed until there are just three left, two on the board and the one the deal or no deal player has selected. My wife believes at the end of the deal or no deal game, when only 3 cases are left, the player has a 1 in 3 chance for the highest prize, assuming that the grand prize has not been seen yet. I believe the true odds are still 22-1, which is what they were when the case was selected. Which is it? Dick D.

Dear Mark,
Do you watch Deal or No Deal, and what is your take on the game in general and when should you take the banker's offer? Cheryl A.

Yes, Cheryl, I've watched Deal or No Deal a bit, although not a lot since I really don't see it as much of a game, since neither skill nor trivia is involved, just an ambiguity, a bellowing brother-in-law, the prickle of greed, and a baseless guess.

My take on it, Cheryl: I find Deal or No Deal excruciating to watch because of its tortoise pace, (an exercise in Job-like patience), not to mention all those dreary commercials to keep the suspense alive (huh?). When they finally return from pushing products, we get to watch five more minutes of a brother-in-law in the wings yelling; "Take the Deal, you Plonker!" Now that everyone knows what I think of the show's staging, plot, and general entertainment value, and because of my resultant limited exposure to Deal or No Deal, I really can't answer your Banker offer question with 100% certainty.

From what I have seen, I am sure that probabilities are re-calculated by the anonymous silhouetted Deal or No Deal banker, based on what values remain in play, which allows me to put Dick's question to bed. At the onset, Deal or No Deal offers the best odds for winning £250k on national TV -- 1 in 22 (or 1 in 26 in most other countries). But once only three cases remain, those odds are improved to 1 in 3. Your wife is right, case closed.

Back to you, Cheryl. From my limited observation of Deal or No Deal, the banker seems to start with offers well below the expected value of the remaining suitcases, getting closer to the expected value near the end. A smart player would refuse the banker's offer until it is close to or exceeds the average of the remaining suitcases. If the Deal or No Deal contestant just wants to maximize the expected value of their winnings they should always turn down the Banker, and yet, it seems most Deal or No Deal players end up accepting the Banker's deal before all the brief cases are opened. So, are they well advised by their brother-in-law to take the money and run? Probably yes, because it seems their decisions are made based on what we call in the gambling business risk aversion.

Given the choice between two gambles: Gamble A making the weak promise of a very high payoff, and Gamble B making a more likely promise of a more modest payoff -- the gambler showing "risk aversion" will choose Gamble B, preferring to take the lesser risk. The "risk seekers", familiar at casino tables, accept a negative expected return or the thrill of financial risk and a possible immense payoff.

Also factored in is that the amount of money involved in Deal or No Deal is a significant fraction of the contestant's net worth. As we crunch the banker's offer in our heads at home in the comfort of our Lazy Boy, the Deal or No Deal banker's stingy offer may be far more than the contestant makes in a year. It's easy to see why many players become risk averse and are willing to accept a sure amount rather than a possibly higher amount by taking additional risks. Let's face it, taking risks is... risky.

Just like those million dollar figures on a progressive slot machine, Deal or No Deal taps into the most basic human emotions: greed, a desire to improve one's situation through a get-rich-quick scenario. It's something we can all relate to, and one we all play in life differently.