Money Grabbing Contest -- Strategy?

[RocketManJames]

Here's a hypothetical money-grab contest I thought about last night before crashing...

The rules:

You and a large sack (for the money) will be put into a room for 15 minutes. In this room, there will be a gigantic pile of money, enough to swim in. There will be $1, $5, $20, and $100 bills. There are 10x more $1 bills than $5. 10x more $5 than $20, and 10x more $20 than $100 bills.

The catch... before entering the room, you must specify the exact dollar amount that you wish to extract from this room in the allotted time. When the 15 minutes is up, they will count how much you have in the sack. If you do not have exactly that amount, you win nothing. If you do, you will win whatever is in the sack.

What would be your strategy once you got in the room? What would your target amount be?

-RMJ

[fnord_too]

Ok, so there is (effectively) an unlimmited amount of bills?

so 1000 1's, 100 5's, 10 20's and 1 100 is the ratio?

This is hard without having a swimming pool of money to do feasability tests in. I think I would go with 8-10k. My strategy would be to count out money in $100 increments and put them in the bag as I get to $100. The keys are to be very careful with your counting, not loose track of how much you have put in the bag, and not to let any loose money fall into or out of the bag.

I think it would be difficult to not screw up, but I think your best risk/reward target would have you counting a $100 in somewhere around 10 seconds. I think you should ignore 1's entirely, as they add too much risk (longer to count them, more danger of miscounting).

[Lazymeatball]

The average bill that you grab will be worth $1.62. If your strategy is to go for a mad dash, calculate how many bills you can grab in fifteen minutes, multiply by $1.62, and pray, as your variance will nearly gurantee you do not get an exact amount equla to your prediction. So I guess the answer to this question is a balance between practicality and greed (maximizing your outcome). You could just predict $100, grab a benjamin, and walk out.

Basically, 0.901% of bills are going to be benjamins. Calculate how many bills you could sift through to find benjies in 15 minutes, then reduce by 20% (this number could be optimized by doing standard deviation calculations and whatnot)to give yourself a comfortable cushion amount, and reach for that amount. If anyone can prove that looking for a different value bill is more worth it, I'd be interested.

[felson]

Let's say it takes 3 seconds to examine a bill, add it to your mental total, and stuff it in the bag or discard it. Then your expected earn is 15 min * (20 bills / min) * ($1.62 / bill) = $486. You need to pick a target that you can be sure you will achieve though, so we need to adjust this downward somewhat. Let's say $440.

Then you just pick up each bill and keep going until you hit $440. Never discard any bill unless it will cause you to exceed your total, and never remove any bills from your bag once they are in there. Since 90% of the bills are 1's, even if you get $439 towards the end, you will almost certainly pick up the $1 you need within four tries.

This approach is superior to any approach which has you pick up a bill and then throw it away. You could improve on this though if you assume that you can glance at several bills at once and pick up the biggest one.

[felson]

[ QUOTE ]
Basically, 0.901% of bills are going to be benjamins. Calculate how many bills you could sift through to find benjies in 15 minutes, then reduce by 20% (this number could be optimized by doing standard deviation calculations and whatnot)to give yourself a comfortable cushion amount, and reach for that amount. If anyone can prove that looking for a different value bill is more worth it, I'd be interested.

[/ QUOTE ]

Actually only about 1 bill in 1000 will be a benjamin. So looking for benjies is not worth your time.

[elwoodblues]

15 minutes is a LONG time and a swimming amount of money is a LOT of money. Pick an arbitrary number divisible by 100 -- 10k is probably a good one, though I think you could easily/accurately get more. Then only take 20's and 100's. Give yourself enough time at the end to do a quick re-count (keep the 20's and 100's in distinct piles in the bag (i.e. add 20's to the top of a stack and 100's to the bottom.) I think it would be pretty easy to get 10k.

[TimM]

[ QUOTE ]
Basically, 0.901% of bills are going to be benjamins. Calculate how many bills you could sift through to find benjies in 15 minutes

[/ QUOTE ]

1 100, 10 20s, 100 5s, 1000 1s = 1111 bills, so it's 0.09%.

1111 bills in wrappers would stack less than a foot high. enough to swim in means there would be thousands of 100s available.

While searching for the benji's, palm 20's as you find them and when you reach 5, book it. Maybe leave a 30 second cushion at the end to recount - better to waste some time than to lose it all.

[ClimbRock512]

I think 10K sounds reasonable. Search for hundreds and stick them in your pocket, stuff as many $20 as possible into the bag as you go. Leave 1-2 mins at the end to count. Dump the bag in the corner, clean floor space would be good. Add the hundreds, and find out how many 20's you would need to get to your goal. Throw them in the bag too.


The idea about examining each bill and adding it is entirely wastefull. $100 bills will be easy to spot and you can quickly sift through lots of bills.

The bigger the room dimensions, the more money you could strive for. If the room is small and very deep, the top wuold eventually become all $1s. You want the pile thin and have a large area on top.

[felson]

10k means you find a benjamin every nine seconds. You think you can look through 1000 bills that fast?

I agree that my ~$400 was an underestimate. But I really doubt that anyone could do above $2k.

[RocketManJames]

Pretty wide range we've got. We have an admitted underestimate for about $400 and some who say $10K. I thought about this a while last night, and really, I have no idea what would be a good "maximizing" target.

I was thinking that I could do basic addition quickly, meaning that I could likely grab and sum more than one bill at a time. Of course, this will increase my chances of makin a mistake and getting nothing at all.

And, although only 1 in 1000 bills would be Benjamins, I think that I'd be able to spot a few openly visible ones quickly. And grab them. Kind of like "Find Waldo" fun.

I think I'd get greedy and say that I think I could get between 5K and 10K.

Keep the thoughts coming. I'm interested.

-RMJ