A Decision Making Error - Easy Question
 

This is the first of several stories I plan to tell about the time I served as Bob Stupak's Resident Wizard at Vegas World. It has implications for many situations.

Upon checking in to the hotel under his package deal the guest had a choice among five "gifts". They cost Bob about twenty bucks though he placed a $200 or so retail value on them.

One of the gifts became unavailable to him. So he had to find a replacement He had it narrowed down to two possibilities. To make his decision he conducted an experiment where only those two gifts were offerred to about a thousand patrons. About 60% picked gift A. So Bob was about to choose that to be added to the five gift menu. I knew what the two candidate gifts were and insisted that he picked the wrong one. (To tell you what the gifts were would be too much of a hint.) He asked how I could possibly go against the statistical evidence. To which I replied what?

Re: A Decision Making Error - Easy Question
 

when there's 2: 60% prefer A, 40% prefer B
when there's 3: 0% prefer A, 40% prefer B, 60% prefer C

ie. it depends on what the other gifts are.

Re: A Decision Making Error - Easy Question
 

and to make it more intuitive, think of it this way:

gift B (40%) might be something that 80% of all women want, but something that 0% of men want.

so 20% of women choose gift A, and 100% of men are forced to choose gift A.

it's easy to see that gift B could be more popular than gift A out of a larger selection of gifts.

Re: A Decision Making Error - Easy Question
 

It would seem you would want to add the less popular gift so that the guests would be more likely to select each gift in an equal amount (thus reducing the chance of unavailability and possibly simplifing reordering if multiple items could be reordered at once).

Alternatively, if for some reason the replacement gifts cost Stupak more than the other four, you would prefer a less popular addition to reduce your costs.

Re: A Decision Making Error - Easy Question
 

DS,

"Beat the Dealer is a good book, Bob, but I don't think you want to be giving it out to your guests as a welcome gift!"

Re: A Decision Making Error - Easy Question
 

Yes.

The combination of the other four gifts dominated the 60% one to a greater degree thant the 40% one.

Re: A Decision Making Error - Easy Question
 

Some people seem to have missed this:

[ QUOTE ]
To make his decision he conducted an experiment where only those two gifts were offerred to about a thousand patrons.

[/ QUOTE ]

One possibility that comes to mind is that the "favorite" is similar to one of the other gifts while the "underdog" is something completely different, resulting in the "favorite" often getting passed over for one of the other gifts (or reducing the likilihood that the similar gift is chosen).

Re: A Decision Making Error - Easy Question
 

The people who prefer gift B prefer it by a large margin, so that the aggregate utility of the hotel guests is higher with B in the mix.

Re: A Decision Making Error - Easy Question
 

[ QUOTE ]
The people who prefer gift B prefer it by a large margin, so that the aggregate utility of the hotel guests is higher with B in the mix.

[/ QUOTE ]

This was my first thought. Adding that gift A is only slighly preferred by those who chose it.

There are dozens of potential answers to this I think though many go outside the obvious intent of the question (for instance gift A is illegal, or somehow racist, or dangerous, etc).

The Beating the Dealer comment was a joke, but there are concievably gifts that would hurt the casino in some way (maybe a travel guide that doesn't rate your casino well, though he's likely not dumb enough to consider that in the first place).

Re: A Decision Making Error - Easy Question
 

POG forum has "Situational puzzle" games - a game where little information is offered in the beginning and participants ask questions trying to recreate the full sequence of events or whatever. The person who starts the game thread answers all questions with pretty much "Yes", "No" or "not relevant") (but is not LIMITED TO these anwers).

With that said -

- Did the more popular gift have any negative expectation (directl or indirect) on the profit of the establishment (i.e. "Beat the dealer", guide favoring other establishments, tickets to a show in another establishment, etc.)
- Did both gifts cost him the same?
- Does EVERY visitor to the establishment ALWAYS choses to take a gift or do some decline?

That's a good start, I think...

The Answer
 

The answer that I was looking for and the one that has general implications was that the gift that lost the head up contest could still easily be more likely to win in a five way contest. In other words many of the 40% would choose it first among five but not so for the 60% who chose the other gift. If I had told you that the losing gift was a Mickey Mantle, (I think) autographed baseball the answer would have been obvious.

Re: The Answer
 

I bet this was when Stupak over booked and two gifts you speak of were 1) an ass whipping in the back alley by security thugs and his ugliest coctail waitress or 2) a shuttle to the thunderbird MOTEL where the dumpsters were cleaner than most of the rooms and you would be staying for the full 3 days of your Free Vegas Vacation at Vegas World.

(I took the ass whipping)

Re: A Decision Making Error - Easy Question
 

[ QUOTE ]
Upon checking in to the hotel under his package deal the guest had a choice among five "gifts". They cost Bob about twenty bucks though he placed a $200 or so retail value on them.

One of the gifts became unavailable to him. So he had to find a replacement He had it narrowed down to two possibilities. To make his decision he conducted an experiment where only those two gifts were offerred to about a thousand patrons. About 60% picked gift A. So Bob was about to choose that to be added to the five gift menu. I knew what the two candidate gifts were and insisted that he picked the wrong one. (To tell you what the gifts were would be too much of a hint.) He asked how I could possibly go against the statistical evidence. To which I replied what?

[/ QUOTE ] If the demand for gift A is greater why not sell it for the inflated retail and offer the gift (B) of lesser interest as a 'free' item. Of course I am assuming that these are gifts that are available in a gift shop hence the gift menu.

Re: A Decision Making Error - Easy Question
 

What was the winning gift?

Re: A Decision Making Error - Easy Question
 

The winning gift was A-Ko, the losing gift was 9-8s.

Now what did Bob say?
A. You are a genius!
B. Leave me alone with your math stuff.
C. Let me think about it.

Re: The Answer
 

[ QUOTE ]
I bet this was when Stupak over booked and two gifts you speak of were 1) an ass whipping in the back alley by security thugs and his ugliest coctail waitress or 2) a shuttle to the thunderbird MOTEL where the dumpsters were cleaner than most of the rooms and you would be staying for the full 3 days of your Free Vegas Vacation at Vegas World.

(I took the ass whipping)

[/ QUOTE ]
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