Moola - Theory and practice?

[ruffilb]

The way it works is thus: You start with $.01. It's basically a pyramid, where you can advance a level and double your money in a 50% chance, or go all the way back down to one cent.

Thus, the probability of getting to level X is .5^X and
The expected value of each level is .5 * 2^X/100.

How does one then calculate the expected value of each play? .5^X*2^X/100? That doesn't even make SENSE to me.

Anyone have ideas for playing the games? Mostly I've just been playing Ro-Sham-Bo, and I have a few strategies for winning that (i.e. playing the winner in the bonus subset when up by a few points), but mostly I just sort of goof around and play as many as possible. I've found that overanalyzation doesn't work too well, so I just go with the flow.

 

[BrownTown]

no clue what your asking, sorry

 

[Codewiz]

I only play goldrush. With goldrush, you can at least know possible ways to win based off previous played rocks.

 

[JoshGuru7]

By RoShamBo you mean Rock Paper Scissors?

Of the problem you detail the expected value of each level is simply $0.01. This is because your rewards double each successful round but so do your risks. For example, the 14th successful step would double 81.92 and have a 1.22E-4 chance of doing so. 81.92 * 1.22E-4 = 0.01.

 

[Loki726]

JoshGuru7 nailed it, the expected value is the same for each level. An interesting note is that the expected payout of playing goes to infinity as the number of levels goes to infinity.

SUM[(.5^k)*(.01*2^(k-1)),k,1,infin] -> infin

 

[ruffilb]

Originally posted by: Loki726
JoshGuru7 nailed it, the expected value is the same for each level. An interesting note is that the expected goal of playing goes to infinity as the number of levels goes to infinity.

SUM[(.5^k)*(.01*2^(k-1)),k,1,infin] -> infin

It seems to me though that since the probability of winning each level is .5, the expected value of each level is what I posted above, but the chance that that expected value is actually applied is what continues to drop.

I think that the .5^X*2^X/100 overall is accurate, and I definitely buy that the expected value of a single play, starting at the beginning, is eventually .01.

 

[Cattlegod]

I just created a sweet excel file to calculate your chances. All you have to do is play ~30 games or so to calculate your average % chance to win (there is strategy so it isn't just 50%) and then measure the time it takes you to play the game. Finally you will need a confidence interval for which you wish to win.

The file I have tells you the % chance to win any given dollar value just by your average % chance to win, how many games you will have to play to win a certain dollar amount given a confidence interval you input and how many hours it will take you to make that dollar amount.

Here is an example:

If you average winning 70% of your games and it takes you 3 minutes per game at a 90% confidence :

10.24
1 - Play 81 games to win 10.24
2 - Spend 4.05 hours playing those 81 games
3 - Make $2.53 per hour

655.36
1 - Play 692 games
2 - Spend 35 hours playing those games
3 - Make 18.94/hour

Now, that is if you are really good at the game and at a 90% confidence (meaning that 10% of the time this will not work out and you will make nothing for those 35 hours). Now, say you are just a little below average

Win 45% of your games, 3 minutes per game and 90% confidence:

10.24
1 - Play 6,762 games
2 - spend 338 hours (14 straight days) playing those games
3 - make $.03/hour

163.84 (I didn't use 655.36 because my algorithm kinda sucks and cuts out after 300,000 iterations)
1 - Play 164,907 games
2 - spend 8245 hours (343.5 straight days) almost a YEAR STRAIGHT!
3 - Make $.02/hour

All in all, if you are winning 70-80%+ of your games, it might actually be worth it to do on your spare time, otherwise, it would be better to just collect bottles from the garbage. If anyone knows where to host this excel file, let me know and I will host it somewhere.


edit: I just ran through it with 80% chance of winning your games:

10.24
Play 21 games for 1 hour to average $9.75/hour

163.84
Play 52 games for 2.6 hours to average $63 dollars/hour! not bad

 

[andyandyandy]

:Q toooo confusing for me

 

[imported_inspire]

Originally posted by: Cattlegod
I just created a sweet excel file to calculate your chances. All you have to do is play ~30 games or so to calculate your average % chance to win (there is strategy so it isn't just 50%) and then measure the time it takes you to play the game. Finally you will need a confidence interval for which you wish to win.

The file I have tells you the % chance to win any given dollar value just by your average % chance to win, how many games you will have to play to win a certain dollar amount given a confidence interval you input and how many hours it will take you to make that dollar amount.

Here is an example:

If you average winning 70% of your games and it takes you 3 minutes per game at a 90% confidence :

10.24
1 - Play 81 games to win 10.24
2 - Spend 4.05 hours playing those 81 games
3 - Make $2.53 per hour

655.36
1 - Play 692 games
2 - Spend 35 hours playing those games
3 - Make 18.94/hour

Now, that is if you are really good at the game and at a 90% confidence (meaning that 10% of the time this will not work out and you will make nothing for those 35 hours). Now, say you are just a little below average

Win 45% of your games, 3 minutes per game and 90% confidence:

10.24
1 - Play 6,762 games
2 - spend 338 hours (14 straight days) playing those games
3 - make $.03/hour

163.84 (I didn't use 655.36 because my algorithm kinda sucks and cuts out after 300,000 iterations)
1 - Play 164,907 games
2 - spend 8245 hours (343.5 straight days) almost a YEAR STRAIGHT!
3 - Make $.02/hour

All in all, if you are winning 70-80%+ of your games, it might actually be worth it to do on your spare time, otherwise, it would be better to just collect bottles from the garbage. If anyone knows where to host this excel file, let me know and I will host it somewhere.


edit: I just ran through it with 80% chance of winning your games:

10.24
Play 21 games for 1 hour to average $9.75/hour

163.84
Play 52 games for 2.6 hours to average $63 dollars/hour! not bad

I may just not be catching on here, Cattlegod, but why did you use a confidence interval for a question dealing with probability rather than inference? Did you mean a variance?

Confidence Intervals are calculated from a sample - they assume that a population follows a T-Distribution (you used 30 trials to approximate it as a Normal Distribution, which is standard practice), and they give the probability that the Confidence Interval covers the mean, not the probability that the mean is in the confidence interval (Not to say that this is your error, but it's just a common misconception).

Since this is a classical question, I don't see where sampling comes into play. I haven't fooled with any of this since May, so you may need to just spell out how you did all that.

 

[Eeezee]

How about some statistics on the best pattern to play if you want to win in gold rush?