Non poker related problem

[jimmer]

This has been annoying me all night.

Last night my wife and I went down the pub with a few mates. At the pub they were playing the "deal or no deal" game. (i think you get it in the U.S aswell). It cost £1 ($2) for a ticket to enter. Then one lucky ticket would be drawn from the hat and that person gets to play the game with a chance to win £100 ($200).

I've never watched the game before and therefore never really understood the rules until the last few minutes. Anyway, this is what happened.

The women gets down to the last 2 boxes. There's £40 in one and £0.01 in the other. She is offered £14.

(for those of you that have never seen the game either; basically she either takes the £14, or refuses and takes a 50/50 gamble on other two amounts)

So my mate looks at me and says "what would you do?"

I then get really confussed with my calculations. I'm thinking that if i was to take the £14, I'd be playing with a negitive expectation as the average amount of the combined boxes is £20. But then I look at the fact that it's a 50/50 chance of winning £40, or losing £39.99.

The end result is I've come to no conclusion what-so-ever.

Can anyone help?

[Ensano]

6$ isn't worth the gamble in this spot...

[Eusebio]

half of the time you will be losing 13,99 and half of the time you´ll be winning 26

thats
0,5x(-13,99) + 0,5x26=
-6,995 + 13 = 6,005 = EV if you gamble

So you are better if you gamble...

but this is not poker... you wont be in this situation hundreds or thousands of times, so the average doesnt really count. You´ll have to decide wether you could need the 14 or not.

[Fat Tony]

Odds-wise you are definitely better off going for it here. The people on the tv show are usually better going for it too, but it's a lot harder to turn down thousands and possibly hundreds of thousands of dollars on a gamble like that. That's why the people on tv have such a hard time time making a decision a lot of the time. Your decision here is really a no brainer given the odds and relatively low amount involved.

[General Sal]

I think it all has to do with "the utility" of the money involved. Like Eusbeio said... you have to decide if you need the $14 dollars.

With $14 you'll have a solid starting bankroll for the .01/.02 NL game they have at pokerstars. Roll that up to $10K.

[golddog]

Correct! Strictly mathematically speaking, play the expected value, and turn down the $14.

The EV is (40/2 + .01/2) - 1 = 20.005 - 1 = 19.005. Sum(Win*probability) - cost.

19.005 > 14, there you go.

At least I think that's right. I took those classes before a lot of you guys were around...

[HalfSugar]

This whole issue is moot from a statisitcal point of view because it is an isolated event. If you could play it 1,000,000 times then it would be a statistical problem but you are there once and once only.

The bottom line as a couple of people have said is - do you need the money that is offered? If the answer is yes, take it. If not, gamble. It is that simple.

[jimmer]

This whole issue is moot from a statisitcal point of view because it is an isolated event.

Yes you're right. This is a key factor in my calculations and considerations.

do you need the money that is offered?

In this situation, winning or losing the £40 was never my concern. I can take it or leave it.

The thing that concerned me was that one day it might be for £40,000 instead of £40, but as it's been suggested, the issue is then about whether i need the money, not the odds.

Thanks Guys

[Eusebio]

Sum(Win*probability) - cost.

true, didnt consider the "entryfee" in my calculation