Where I'm likely to be ranked?

There are a total of 200 contestants.
Each person holds an RNG device that generates random numbers ranging from 1-100.
Every person generates the number 3 times. All 3 numbers will add-up, then compare the total with each other, the higher the number the better.
The total prize pool is $1175, the prize structure is as follows:

1st $100
2nd $50
3rd $25
4th $15
5th $10
6th-200th $5

In this situation, my EV is simply $5.875. ($1175/200=$5.875)

What if I get to generate the number 4 times, drop the lowest number, use my 3 highest numbers to compete with 199 other contestants? What my EV would be in this situation?

Quote: ReyGarcia

There are a total of 200 contestants.
Each person holds an RNG device that generates random numbers ranging from 1-100.
Every person generates the number 3 times. All 3 numbers will add-up, then compare the total with each other, the higher the number the better.
The total prize pool is $1175, the prize structure is as follows:

1st $100
2nd $50
3rd $25
4th $15
5th $10
6th-200th $5

In this situation, my EV is simply $5.875. ($1175/200=$5.875)

What if I get to generate the number 4 times, drop the lowest number, use my 3 highest numbers to compete with 199 other contestants? What my EV would be in this situation?

Interesting question. Just to be clear, the other 199 contestants get 3 randomly selected numbers from 1-100, while you get 4 randomly selected numbers from 1-100. There will be someone here who will figure it out..... above my pay grade...... I'll guess an EV of $7.

Yes.
199 contestants get 3 random numbers, add-up all 3 numbers.
I get 4 random numbers, drop 1 lowest number, add-up 3 highest numbers.

Integers? Then, problem of ties.
Better do it with continuous numbers. Also, the math is easier.

Well... easy it ain’t!

Simplifying: random draw on a uniform [0,1]
A single player score X is the sum,of three independent uniforms. Distribution is awkward, graph like a jellyfish / ghost , formula in three quadratic parts.
The multivariate distribution (X1, X2 ... X199 )is the product of those.
But we want the ranked scores. Their distribution is horrible. Even the univariate distribution of the maximum is hardly analytical.

As for your score, it requires to compute the ranked distribution of your four draws, then that of the sum of the three first ones. Also un manageable.

But then, you want the probabilities of this score to fall inbetween the six first components of the multivariate !...

Humm... Forget it.
Try Monte Carlo simulations

50,000 simulations in Excel.
(I know I know, this is no legitimate RNG. But hey! This isn’t a life-and-death matter either, huh?)

EV = $7.8164
Average score = 1.800216 (multiply by 100 in the original [1 - 100] setting)
Average 1st score = 2.72483
Then 2.63243, 2.57074, 2.52274 and 2.48273.

The fact is, your procedure increases average but reduces variance. Makes me think of the obsession of Wizard with House edge, without a look at variance.
😁

That's impressive, the EV seems on par.
I never know excel can do simulation, could you drop a link for the relevant tutorial video?

Quote: kubikulann

50,000 simulations in Excel.

1 ran mine 100k

Quote: kubikulann

(I know I know, this is no legitimate RNG.

I always use a legitimate RNG in Excel. there are a few to choose from.

Quote: kubikulann

EV = $7.8164
Average score = 1.800216 (multiply by 100 in the original [1 - 100] setting)

my sim data: EV = $7.85
Average score = 181.6

I had something like this already for 100 players and top 10 prizes. forget where it came from.

Quote: ReyGarcia

I never know excel can do simulation, could you drop a link for the relevant tutorial video?

Simply compose the necessary cells for one sampling, with a handful of ‘result’ cells.
Make sure the calculations option is‘’manual’’.
Record a macro beginning with Calculate Sheet, then add up the results using Copy/ Paste Special Add Values in some specific cells.
End recording, complete the macro with a loop for as many trials you desire, save.
Run the macro, go take a shit, come back. Divide the sums to get averages.

I’m too old to know how to produce a tutorial video. Anyway, I still use my preferred version, Excel 2000. 🙄😌

Quote: 7craps

I always use a legitimate RNG in Excel. there are a few to choose from.

Could you tell us where to find them?

Quote: 7craps

Average score = 181.6.

Actually, since I worked on a [0-100] range, we must add 0.5 to my result 180.02 to compare with integers [1-100].