Not sure if this is the right place but...

[oriz123]

Hey all, I have a question related to statistics but I think it might go a little deeper than that? I dunno you tell me...anyway lets assume we have chances of winning "something" anything...can be the lotto or whatever. We have A, B, C, D, E and each have a different chance of winning. We will also give them each a value, and the chance of winning improves linearly depending on that value. A has the value of 1,000...B has the value of 3,000...C has the value of 10,000...D has the value of 30,000 and E has the value of 100,000. So in the simplest form with just those 5, for example A would win 0.691% of the time, B would win 2.07% of the time, C 6.9% of the time, D 20.7% of the time and E 69.1% of the time(roughly...I rounded them so might not be 100% exact).

But here's where things get more complicated: what if, in each group, we had more than one? So, say we have 300 of A, 200 of B, 100 of C, 100 of D and 90 of E. Toegther we have 790 now and they are variable, they can change...in an hour it can be 250 of A, 200 of B, 110 of C, 100 of D and 85 of E for example. How do we, at each point in time and in real time, figure out the chance of each of the 790 to win?

 

[tkhunny]

You'll have to give us some sort of indication of how the winner is chosen - and when.
You'll have to provide a better description of what you want. Perhaps you could solve it with only A and B - ignoring C, D, and E?

Give it a go.

 

[oriz123]

Hey, thanks for your reply. So the winner is chosen randomly, based on their value. Basically since it's linear, 100,000 will win 100 times more often than 1,000. Hence why in my previous example A got 0.69% of the time whereas E got it 69% of the time. Together with the inbetweens of B, C and D we reached 100%. The problem is when you have more than 1 each of A, B, C, D and E. Then they each have a smaller chance at winning, but the ratio should remain the same.

I'm not sure if this can be solved with only A and B. Ok lets pretend for the sake of the example that the winners win coins. If we had 100 coins in the previous example(instead of percentage), A would only win 0.691 coins for every 100 coins whereas E would win 69.1 of them. Now lets pretend we have 300 A's, 200 B's, 100 C's, 100 D'c and 95 E's. We also have 300,000 coins. How do you figure out the ratio of each​ of the 795 participants and their chances of winning(or how many coins they're going to win for each 300,000), while still keeping it linear and the same as before?

 

[stapel]

Hey, thanks for your reply. So the winner is chosen randomly, based on their value. Basically since it's linear, 100,000 will win 100 times more often than 1,000. Hence why in my previous example A got 0.69% of the time whereas E got it 69% of the time. Together with the inbetweens of B, C and D we reached 100%. The problem is when you have more than 1 each of A, B, C, D and E. Then they each have a smaller chance at winning, but the ratio should remain the same.

I'm not sure if this can be solved with only A and B. Ok lets pretend for the sake of the example that the winners win coins. If we had 100 coins in the previous example(instead of percentage), A would only win 0.691 coins for every 100 coins whereas E would win 69.1 of them. Now lets pretend we have 300 A's, 200 B's, 100 C's, 100 D'c and 95 E's. We also have 300,000 coins. How do you figure out the ratio of each​ of the 795 participants and their chances of winning(or how many coins they're going to win for each 300,000), while still keeping it linear and the same as before?

What does your textbook mean by "keeping it...the same as before" when clearly you're changing things? When you reply, please include the full and exact text of the exercise, the complete instructions, and any other information that you feel may be helpful for us in trying to figure out what this exercise is asking of you. Thank you!

 

[oriz123]

Oh is this forum just for exercises/homework? if it is, my apologies I wasn't aware. this isn't some exercise I was given, it's something I'm trying to come up with myself for a blockchain project and just can't figure out the right equation. If it helps, just for the sake of the example we can change it from linear to something else. Say we have group A, group B, group C, group D and group E. ANYONE in group B has 5 times the chance of winning than anyone in group A. ANYONE in group C has 10 times the chance of anyone in group A. Anyone in D has 15 times the chance and in E 20 times the chance. The number of people in each group varies all the time(as well as the total), and we have to keep the same ratio at all times. How do we track/ensure that happening, even when the number in each group and the total number keeps changing?