Empire VIP Club Math Problem

[Festus22]

Strictly for curiousity purposes (although the result may be somewhat useful), how would you solve the following:

Empire rewards VIP points based on the square root of the number of hands played per day (I think this is right and if it's not, let's assume it is /images/graemlins/tongue.gif). What is the number of hands/day that minimizes BOTH the total number of hands necessary to reach 5000 points AND the total time it takes to get there.

For example, if you play 1 hand/day, you would only need 5000 hands total but it would take 5000 days. If on the other hand, you play 12,000 hands/day, you'd get there in 46 days but would have to play 552,000 hands.

At what point are the days and hands at a minimum relative to each other?

[Copernicus]

You need to clarify your question. You cant "minimize both". You can minimize the number of days (1 day, 25 million hands) or number of hands per day (1, 5000 days)but "minimizing both" has no meaning.

[TomCollins]

What is the probability the Festus understands basic math? 0%

[Cerril]

I can't remember what you call it either, but it's probably not relevant. Playing for points doesn't have much value, you're better off just treating them as a side thing. From a math perspective it's probably better to just figure out the value of each hand in terms of points.

I'd started charting it out here, but really you might as well just do a log(2)x graph and pick the point that looks the most appealing to you.

A more advanced and useful method would be to go the Points store and get a rough idea of the cash value of a VIP point, then chart out where (v) is the value

(v) / (x^2 - (x-1)^2)

That'll give you an idea of the point you're looking for, I suppose.

[Festus22]

I thought the line "relative to each other" pretty much explained what I was asking.

For example, if I play 400 hands/day, I get 20 VIP points and it takes me 250 days to reach 5000. If I play 800 hands - a 50% increase - I get 28 VIP points (a 40% increase) and I get to 5000 in 177 days (a 29% decrease).

Is there a way to optimize one's playing time to get maximum VIP "value"?

[TomCollins]

Define optimize in a way that makes sense. Optimize relative to each other makes 0 sense.

[Cerril]

Yeah, I think this comes down to framing as much as anything. He'll need to establish the value of a 'point' in $, then figure out the minimum hourly rate he wants to win points. Then you can 'optimize' things.

[Copernicus]

The "optimal value" would depend on the cost of a point vs the value of a point. If you are a winning player points are "free", and you should be maximizing your playing time, regardless of points. It is only if you are a losing player but points somehow turn you into a winning player than you would minimize the number of hands you play..ie 1 a day.

[Duke]

I'm still trying to come up with a good way to frame this question so that I can answer what you "really mean."

When I figure it out, I'll post. I think I have some ideas.

~D

[cockandbull]

i think he's asking what his economy of scale is. i have no idea what to call it other than this. think its like if i can sell this many apples at this price and this many at a lower price, how can i make the most money or such. this is most probably as useless an answer to the answer of what does his question mean.