April 28, 2006
Deal or Fold?
by Luckbox
You've just been offered $129,000 for a silver case with a big number on the outside and an amount of money ranging from a penny to a million dollars on the inside.
$129,000 is more than you've ever made in your life. It will solve every money problem you currently have. The bills will all be paid. The car will be yours. You can travel, you can treat your friends and family and you can gamble worry-free.
And you say, "No."
It's a game show that better demonstrates the human nature of greed even more than the short-lived game show named after the deadly sin. Of course, that old game show featured our own Joe Speaker, but I digress. And this time, we have a shiny-domed Howie Mandell instead of Hall of Fame host Chuck Woolery. Yet again, I digress.
In case you haven't seen, Deal or No Deal features 26 cases with amounts ranging from a penny to a million dollars. You select a single case which is yours if you keep it until the end. Then you begin opening the rest of the cases which eliminates the possibilities of those amounts being in your case.
Periodically, the "banker" tries to buy your case from you based on what's probably a rather simple formula that factors in the dollar amounts still in play. In other words, pick a bunch of cases with small amounts and there's a better chance your case has a big amount and, thus, you'll get a higher offer from the banker.
When the game gets down to about a half-dozen cases or so, the game gets really interesting. I sit on my couch and think, "How could they turn down more than $100,000?" But then I realize it's a lot easier to say that when I'm not the one staring at the possibility of five or ten times that amount.
And maybe that's the mindset we face at the poker table on a regular basis. How many times have you looked down at the nut flush draw, faced an all-in that gave you the wrong odds, and yet you called anyway? How many times have you faced an all-in reraise while holding pocket Q's and had to decided to risk it all on a hunch?
Humans are greedy by nature. Americans are greedier than most. Poker players are the greediest of all. We see that flush draw and imagine the possibilities. We see that big pocket pair and think it can hold up. We're often thinking less about the cards and more about the pot. It's in our nature.
The best poker players fight this urge. Greed is a powerful force. And in many cases it pays off. But then you have to ask yourself: Do I lose more the times it doesn't pay off than I make the times it does?
It may not have the ring of "Deal... or No Deal?" But it's a question that may save you a little money at the tables.
As with many things, it's all about expected value. The offers that the bank gives on that show are below the expected value of the remaining unopened cases.
But here's the catch. Expected value only means something if you're going to have enough trials so that the law of large numbers holds.
For example, in blackjack, always hitting hard 16 on a dealer's 10 is a higher EV than not hitting. And because you can do that several hundred times over the course of a lifetime, you can be sure you're making the right decision.
But on "Deal or No Deal," you're on that show once. So variance reduction does matter. And taking the deal, if it's close enough to the EV of the situation at large becomes a no brainer.
Deal.
My wife introduced me to Deal or No Deal via the online version that you can play for fun. In that one the banker's offer was basically the average of the remaining cases with a little variance thrown in for good measure.
I was going to write the same thing that Bad Blood wrote. You only get one shot. It like what I like to call "The Devil's Wager". The Devil comes up to you and offers to flip a three sided coin versus all of your eartly possessions. If you win he will double your net worth. If you lose you lose it all. You have 2 out of 3 chances to win. Do you take the bet?
Deal or No Deal is a study in results-oriented thinking and expected utility.
It pains me to hear someone say "you should have taken the deal" when it turns out they get unlucky. From an EV POV it is always to the player's advantage to not take the deal.
This is where expected utility comes in. For a player, is it better to take the sure thing of $120k when you only have a 1/4 shot of tanking your deal? The answer here is really what the money means to you.
I'm probably weird, but I think a struggle of mine is being embarrassed by making the wrong decision. BadBlood's observation recently that you need to have your hand caught in the cookie jar occasionally really resonated with me. Even Raymer's advice of making the right decisions and then living with it is somewhat a cop-out, a way to distance oneself from what happens during play and the ultimate result.
What is most interesting to me about the game is how it highlights the marginal utility of money. It might be -100,000 EV to take a deal for 200,000 given the amount available in the unopened cases, but like in your example, it might that the 200,000 cures a lot of your problems, a potential 500,000 only a few more and 50,000 will leave you in your misery.
I am usually screaming deal at the poor old woman with the 7 kids hecause just thought of her next two briefcases opening with tons of zeros makes me cringe. People with a significantly higher income would generally be advised to refuse all the deals as as far as I can remember, they are always less than the EV of the board.
I think this maps most closely to bankroll management, illustrating the concept that when you are playing for more than your bankroll warrants, it may become rational to make sub-optimal EV decisions, particularly when a big swing will knock you out of contention. This doesn't always mean you should always avoid playing above your bankroll level--it may be that other factors make up for the effect--but it puts a good gloss on why being that tight-weak guy who sneaks a lot of small pots and generally avoids the big one may not be making the mistake it may first look like.
I'm left wondering what drugs they pump through your TV to get everyone to watch.
And yes, I watch every Monday.
One of the few times I watched I couldn't believe they took the deal. Let me lay it out.
There are six cases left with values of 1,5,10,75,300,400. They are offering him 100 to take the deal. There is a 66% chance they'll eliminate one of the small cases thus increasing the Deal and give them a 40% chance of big money.
Am I the only one that would 'peel one off' here?
They took the deal for 100 then rabbit hunted. The next case was a dud, deal of 130. Finally getting to his case, you guessed it, 400.
You guys run one of my favorite poker blogs, but this has to be your worst post ever.
Not only is the amount being offered almost always below your EV, but all you need to do is refuse the deal and as long as ONE of the top 3 or 4 cases remains the offer the banker gives you continues to climb.
Only when you are down to 4 or 5 cases remaining should you EVER consider the deal, as it's always a -EV deal and it's very unlikely you will eliminate all cases valued above the offer.
Am I crazy or do you guys have terrible strategy for Deal or no Deal?
Worst post ever? I'll have to check our archives. I know I can top it! :-)
My post really wasn't about Deal or No Deal strategy. It was about how this concept applies to poker, either individual plays, or as others have pointed out, bankroll management.
I would agree with you that, in most cases, you wouldn't take a deal until you have 4 or fewer cases to choose from.
Ok, that was harsh of me, but I find the contestants on that show staggeringly bad at even a qualitative analysis of how to maximize their return.
Of course, working in television I also understand that's why their on the show in the first place.
NEVER take the deal until you are down to 5 or less cases OR the top three amounts are all gone.
I saw an episode about a month ago where I would take an early deal. The player in the first several rounds managed to eliminate almost the entire left side of the board, getting a deal of 120k on the table. However, to continue he had to open 3 cases. I would take this deal even though it is easy in the game, because there are many outcomes that tank my deal at this point.
