On Let’s Make A Deal, what is the mathematical formula that the Banker is using to figure out how much money to offer? I can’t seem to crack it…
I’m not sure there is a clear formula.
It’s generally a function of X, which is the expected average outcome of playing the game to its conclusion and Y, the number of rounds that have been played. The offer approaches X as Y increases; early on the banker is offering an insultingly small fraction of X (since the game would be boring if anyone took the first offer) but as the game progresses the offers get closer and closer to X and in the odd case actually exceed it a little.
I suspect they will adjust Y up and down a little depending on how much of a sucker they think the contestant is.
Are you talking about Let’s Make a Deal, or Deal or No Deal? They’re two very different shows. I’m assuming the latter from context, but RickJay answered your question without batting an eye, so I’m wondering…
Deal or No Deal. I’m a twit.
Thank goodness. I was terrified that you were going to ask what were the odds that trading your first pick away for the curtain Carol Merrill was standing in front of would improve your outcome.
I’ve corrected (and added to) the title of your thread, Reyemile.
My wife used real examples from several shows to try to come up with a formula. She could find no consistent single formula that fit every show. Though she admits that there could be information not available to her that could help develop a formula that would work. For instance the show producers may have set arbitrary minimum offers or any other such variable that is set for reasons other than odds-making. My wife thinks the banker uses some type of algorithm as a guide but uses his discretion to adjust the offers based on the emotional state of the player.
I think most often in the later stages, lately anyway, that the deals offered are closer to “correct” expected value when there is a “safety net” in play, eg. the board has $400k, $200k, $1k, $500, $10, $1. The EV should be around $100k, and the offer might be around $80k.
But then if the player eliminates the $200k, EV only drops to around $80, but the deal offered can drop insultingly low, to maybe $35k or so… total BS.
But I agree that I don’t think there is any set algorithm. They mostly try to make for good TV, but I tend to think they also err on the side of tightwads.
Furthermore… suppose I’m on that show.
On the board are $1,000,000, $100k, $10, $1. My EV is $275k.
The offer is probably unreasonably low, like, $150k.
I take the [bad] offer, without a second’s reflection. I simply cannot afford to gamble at these stakes, even though the gamble is highly in my favor.
I can really use that $150k. It pays off my house, pays my daughter’s tuition, etc.
Suppose the board is $50k, $10k and $1. The offer is $15k. Again, I take the deal. My EV is only $20k, and I would not take $15k to Vegas hoping to win $50k
Now then, suppose we’re down to two numbers $10k, and $1, and I’m two months behind on my $800 mortgage. The offer is $4k. I still take the $4k, because I would never put $5k down on “RED” in one turn of the roullette wheel. I’d take it down to maybe $3k even, because I’m dirt poor right there.
Get it so far? I’ve been taking bad deals left and right, because these are sums that I could not justify LAYING DOWN ON A CRAPS TABLE IN VEGAS.
That said, if I had $5,000,000 in the bank, house paid off, etc…
Board is $500k, $100k, $1, offer is $150k… (EV=$200k)
There, I take the gamble.
In the UK version, the Banker sometimes picks up on a chance remark (‘my lucky number is 12’) and offers say £12,012.
“My lucky number is one billion!” 
RIP 
Yes, but that’s a REALLY bad deal. Look at the results:
- You pick the 1,000,000. EV drops to $35K. You lose $115K.
- You pick the 100K. EV goes to 330K. As you get closer to the end, the banker offer usually gets closer to the expected value. So you probably get offered something like $310,000. You gain $160,000.
- You pick $10. Roughly the same result as above.
- Roughly the same as above.
So you have 3 chances of walking away with at least $300,000 and one of walking away with $35,000.
But it gets better for the player. Because if you knock out one of the two smaller picks on that round, you now have another decision. If you play on, on your next pick you have two chances to run the EV up to $500,000, and one that would lower it to about 50,000.
With those kinds of odds in your favor, you really need to have a steep utility function to turn down the offer. It would be a different matter if it was $1,000,000, $50, $10, and $1. Now you are always at risk of being wiped out completely, so the variance goes way up and your risk aversion should lead you to take a smaller offer.
But you aren’t at a craps table in Vegas. You’re in a once-in-a-lifetime opportunity to start from nothing and parlay a set of winning to a truly life-changing amount with the odds heavily in your favor. Under these conditions, you should tolerate far more risk than you would on an average holiday at the craps tables, especially when the odds are in the houses’s favor in craps.
I’m a very cheap gambler. If you ever catch me playing a slot machine, I’ll put putting nickels in it. I feel queasy if I bet more than a few dollars at a time on anything.
However, when I’m playing poker, I’m confident that I’m a winning player over the long term, so it’s much easier in the short term to divorce myself from the reality of the money on the table and what it means to me. I’ve won and lost thousands of dollars in a single pot, and not be bothered by it. Than an hour later agonize over whether I should have a hamburger or splurge and get the steak sandwich.
If you go on a show like Deal or No Deal, you have to walk in with that attitude. The odds are in your favor, you’re getting an opportunity, and you’re going to throw caution to the wind and take your best shot at grabbing as much as you can. That doesn’t mean to be stupid, but to make coldly logical choices without thinking about what the money really means. That’s your best chance of maximizing your profit from the game.
isnt the game pure odds? nothing complex to it that I can see at all. (yeah I know you were talking about the bankers offer in the op)
my roomate watched this a bit and from the comfort of home its very very easy to take a look at the odds and say when you should take the money and run, based purely on whats left to eliminate.
Those are very good points, Sam.
I’m just saying that if all I had in the world was $150,000… I simply couldn’t gamble $115,000 of it (with a wife and daughter) even with 3-1 odds to double or almost triple it.
The risk of ruin is just too high for me there. If I had another $150k in the bank at home, sure, no problem.
… furthermore, I tend to doubt that the next offer would be $35k with $100k, $10, and $1 on the board.
I’ve seen it WAY insultingly low in that spot… more like a $10k offer, at which point I can afford to say “screw you”.
I agree with Sam Stone if the idea is to try to win as much s possible.
And this is a logical exception. If a certain sum of money will clear your debts / let you take your family on a holiday they really want / buy your partner something special / allow you to move to a better neighbourhood etc:
then that specific sum is a bigger priority than winning as much as possible by taking reasonable risks.
These kinds of questions are what makes the game interesting. It’s NOT just about the odds. It’s about variance and utility. Everyone has a different utility function. Obviously, if you needed 80K for a life-saving operation, you’d be an idiot to take 80K in winnings and risk it for almost any reason at all. On the other hand, if you’re already worth millions, you would be a fool to turn down an opportunity to double up 80K if the odds are 2-1 in your favor. In this case, the marginal utility of the 80K makes little difference in your life, so your decision should rely more heavily on the true odds of the play.
Or put in a way we mortals can understand. Someone offers you a deal to flip a coin, and if it’s heads you pay $5, and if it’s tails you get $10. Would you take the deal? Almost anyone would. Now let’s change the values: Heads, and you have to give up your house. Tails, and you get two houses. The odds are exactly the same, but the risk of losing your home may be so intolerable that you can’t play.
But as you later admit, it’s about utility.
Given a gamble between 3 shots at $300,000/1 at $35,000 or $150,000 straight up, I have to admit I might go with just taking $150,000. The marginal utility, to me, of the delta between $35,000 and $150,000 is MUCH greater than the difference between $150K and $300K. In my current financial situation that $115K is just enormously, enormously valuable. Now, had you asked me ten years ago I’d have had a different answer, and five years from now might also be different. You can construct any number of scenarios where I should logically bow out of the game and avoid further risk, and any number where the right strategy is to tell Howie to shut the hell up and open another case. As I’ve written before, I would be the worst contestant ever:
HOWIE: Okay, so Rick, you’re from Burlington…
ME: One though six.
HOWIE: Huh?
ME: Open cases one through six. Now.
HOWIE: But, you…
ME: (Yelling past Howie) Hey, you! In the skanky dress! Open the fucking case! Good, ten thousand. Now you! Open it up!
But to be honest, this is a close call. $35K is, after all, not a kick in the balls by any means, and there IS significant utility in that $150K/$300K delta. But I gotta tell you, I’d forever regret losing $115K, whereas I wouldn’t feel so bad about getting $150K instead of $300K.
Total all the money amounts on the board. Divide it by number of cards left. That is the starting point.