Deal or No Deal Maffs

[surviva316]

been too busy for poker and poker study for the past few weeks due to term papers, etc, and felt like easing back in with a laid back discussion on poker maffs applied to other games.

deal or no deal is a game show we have here in america (and elsewhere, i presume) whose general rules you can find on your own because it's easy to find, easy to learn, and too much work for me to bother explaining here.

let's say that you are down to two suit cases: the one with $0.01 and the one with the $1,000,000 (the one penny and the one million). the banker offers you n dollars for your suitcase.

how large does n need to be for you to accept the deal?

let us say that in this hypothetical, this will be your one and only appearance on this show and your only time playing any sort of equivalent game in your lifetime. you are a fresh out of college kid destined for middle classdom (100k in college debt, degree in education, married to an english major, no money bags parents, etc)

[couriermike]

ideally n should be the expected value of getting to choose between the last two cases, or about 500k, but since this is life-changing money and the marginal value of the money is decreasing, i'd take alot less than that. if he offered 400k, i'd snap accept.

[Openside]

I have 50% equity

n/1000k = 0.5
n=500k
therefore if n<500k decline the deal.

Edit:

let us say that in this hypothetical, this will be your one and only appearance on this show and your only time playing any sort of equivalent game in your lifetime. you are a fresh out of college kid destined for middle classdom (100k in college debt, degree in education, married to an english major, no money bags parents, etc)

Applying this to poker; you are not br for this so take your money and run. DEAL!

[spoonitnow]

Taxes matter too. The first dollar you make is going to be taxed at a lower rate than the 50000th which is going to be taxed at a lower rate than the 200000th. This skews it even more in favor of lower numbers.

I have 50% equity

n/1000k = 0.5
n=500k
therefore if n<500k decline the deal.

This is wrong because the first dollar is worth more than the 500000th, even without considering taxes.

A neat example is if the n+1 dollar is always worth 99.9999% of the n dollar, then if the first dollar is worth $1, then the 500000th dollar is worth about $0.61 and the 1 millionth dollar is worth about $0.37.

ICM is related to this.

[Donachello]

Spoon is right and like surviva mentioned it's way way dependent on your own situation. Personally, if I had a great first round of picks ie. eliminating the .01, 10, 100, 500 or something I probably wouldn't be playing very long.

[spoonitnow]

Spoon is right and like surviva mentioned it's way way dependent on your own situation. Personally, if I had a great first round of picks ie. eliminating the .01, 10, 100, 500 or something I probably wouldn't be playing very long.

Bout tree fiddy.

[Penneywize]

So, Spoon sort of alluded to this but I figured I'd put in my own two cents anyway - this all has to do with risk aversion.

Essentially, the reason the "bank" doesn't just offer some number arbitrarily lower than the average of the remaining suitcases is because they are aware of the fact that individuals are risk-averse; they can offer the contestants a sum significantly lower than the expected value of the remaining brief cases and still reasonably expect that offer to be accepted.

Without getting too pedantic (hopefully) here's a graph of log utility; a classic representation of a risk-averse individual's utility function:


The gist of it is that individuals value the marginal dollar less than that of any of those previous, as Spoon (and courtie, apparently!) pointed out. The implications are pretty interesting however. On a basic level, consider why a billionaire would probably not bend over to pick up a 5$ bill if he came across one on the street one day, while poor students like myself wouldn't think twice about it.

More generally, it explains why sometimes, individuals will not accept a bet even if it is significantly +EV. Think of this: if for some reason you found yourself at the Bellagio and Doyle Brunson walked up to you and offered to give you $200,000, but also said you could put that money up against him in an all-in preflop matchup of your AK versus his QJ. You're a 65 to 35% favourite, but I would submit that most of us - those of us with incomes less than say 150k / year - would happily take the money and gtfo.

The reason for this is that the amount of utility we would gain from winning that hot-and-cold matchup, based on the graph above, is vastly lower than the amount of utility we would lose if things didn't go our way.

And so, a +EV bet will not always be accepted. From here it's pretty easy to see why, on Deal or No Deal, people often (correctly) accept offers that are significantly lower than the expected value of what's left in the briefcases.

As for the question in the original post, I'd snap accept any reasonable offer the bank made, 300k and up.

[couriermike]

When your friends say, 'You could have had a million dollars!' Just say, 'Or I could have had nothing...like you.'

[rong]

As for the question in the original post, I'd snap accept any reasonable offer the bank made, 300k and up.

So 275k is a refusal?

[HarleyGuy13]

I would like to buy a vowel plz!

[Imthenewfish]

i see ICM'aments but dis aint no sng or tourny!

[Icanhastreebet]

Sell some action if they offer you less then 300k, otherwise just take 300k+.

[Penneywize]

Sell some action if they offer you less then 300k, otherwise just take 300k+.

This man knows how to think! I like.

[OngBonga]

I'm in the UK, so I would attack the host Noel Edmonds and probably forfeit any prize.

[surviva316]

ok, so when it's a coin flip, you're willing to sacrifice many ev's to cut variance, so let's try a less variant scenario.

Scenario #2

same hypothetical person from before. same circumstance that this is going to be the only time you're going to play the game, etc etc, ldo.

You have 6 briefcases left and are being offered n dollars for your own briefcase. if you decline, you will be offered another deal after opening 1 more briefcase.

the possible amounts that are left are:

$400,000
$75,000
$5,000
$500
$75
$25

now, how large does n have to be for us to accept the deal?

[Openside]

Scenario #2

We have a 1/6 chance to win a max. of 400,000.

1/6*400,000 = 66,666

So if n> 66,666 DEAL!

[surviva316]

We have a 1/6 chance to win a max. of 400,000.

1/6*400,000 = 66,666

So if n> 66,666 DEAL!

variance discussion aside, this isn't correct.

[couriermike]

/We were watching this show last night and my brother tells me Howie Mandel is a germophobe and that's why he always does the fist bump.

[couriermike]

The expected value of the game right now is (400k+75k+5k+500+75+25)/6 = 80,100.

Oddly enough, the current expected value of the game when you decide to decline the deal and choose/eliminate one briefcase, doesn't change, because it's the average of the six expected values you get from eliminating one briefcase at a time, which averages out to the same as the above.

So the only real question is, will the banker's offer go up or down if you choose no deal. Well, 5/6 of the time it should go up because 5 of the 6 briefcases contain amounts less than the current ev of the game. The only question is, is that increase worth more to you than the one-sixth chance of eliminating the 400k and radically decreasing the banker's offer and value of the game, for the rest of the game? Again, a personal decision, but probably not.

Having watched this show alot, if I got an offer of 200k in the later rounds, I'd def take it. Alot of the people 'playing to win', turn down 6-figure offers, and wind up going home with hundreds, haha.