Not exactly a homework,
but I figured out the formula that gives the chance of winning 12 games in arena in hearthstone (winning 12 games without loosing more than 2), given X = win rate

I want to figure out what winrate you need to win 50% of all arenas played

The formula is:

78X^14 - 168X^13 + 91X^12

The equation I need help solving is this:

78X^14- 168X^13 + 91X^12 = 0,5

This post was edited by Dragon_Reborn on Oct 14 2015 01:21pm

I'm confused. You are just asking "how many games do I need to win in order to win 50% of the games".

Dunno about you but ... it sounds like half to me

No, please read the following if I wasn't clear in OP:

I want to know what my winrate (X in the formula) needs to be to win every other arena I play (Winning 12 games, without loosing more than 2).
(if you don't know hearthstone this information in my OP might be misleading).

Basically I want the equation I posted solved.
Or rather, if possible, explained how to solve the equation.

This post was edited by Dragon_Reborn on Oct 14 2015 01:21pm

Without looking at the formula, I can tell you that your winrate needs to be 50% or better to win 50% of the games or more, given a very large number of games.
However, statistics and probability are a lot more complicated than that. I don't know how you came up with that exponential formula, but you can't just say "I need this winrate to win 12 games out of 20" or whatever. You have to consider confidence in the result, because you are never guaranteed those 12 wins. You can ask questions like "If I have a winrate of 60%, how likely is it that I will win 12 games out of 20?", assuming that your wins follow some sort of a known distribution.

Having said all that, the value of X that satisfies your expression is approximately 0.813526

This post was edited by russian on Oct 14 2015 02:58pm

I would like to know how you got your equation which shows you win 12/14 battles which constitutes a win. I don't think Initial equation is correct.

formula's wrong

Very wrong I don't think he understands the laws of probability very well.

Can you show how I can arrive at this answer (without the use of a calculator - just pen and paper)?

I tried doing this, but most of the math I use I have to go 10 years back in time and work with my high school math meh.

Also I think you have the wrong idea of what my formula is for. Please read what I'm trying to do again.



Why do you say formula is wrong? Do you understand what the formula is for, as above read again carefully, instead of just talking down on people.
I don't have the advantage of using sophisticated math, so I have to work with a basic understanding of numbers and probablilty.
Which I did, and I'm confident I got the right formula.
If anything why not do as the guy in the quote below, try to contribute and ask me to post work arriving at my formula (if you have doubts - I know you are the same guy, but don't shit on people please)?



I think you understood what I tried to do with my formula. But just to clearify:
The formula shows my statistical chance of winning 12/14 battles, which constitues a win

I did very simple work with it. I started with the formula:

chance of 0 loss:
variations: 1
1 * X^12

chance of 1 loss:
variations: 12
12 * X^12 * (1 - X)

chance of 2 loss:
variations: 78 (to simplify calculation I did 12 * 13 / 2 ) (why? because variations include: 12+11+10...+1)
78 * X^12 * (1 - X)^2

formula:
X^12 + 12X^12(1-X) + 78X^12(1-X)^2 =
X^12 + 12X^12(1-X) + 78X^12(X^2 - 2X + 1) =
X^12 + 12X^12 - 12X^13 + 78X^14 - 156X^13 + 78X^12 =
78X^14 - 168X^13 + 91X^12 = STATISTICAL CHANCE OF REACHING AT LEAST 12 WINS OUT OF 14 GAMES GIVEN X = WINRATE FOR EACH GAME



Now if any you still say this is wrong, I would like you to explain where I went wrong, but I doubt it, as I'm not stupid and can use my brain even though I don't know advanced math methods.
If anyone have a simpler formula that would still give the correct answer, I would love to see it and how you arrive at the answer.
Still would like to see the method of solving my original equation though. (still not answered, just toxic shitters not trying to help - only 1 guy answered what I asked for, and was nice providing info as compared to others)

This post was edited by Dragon_Reborn on Oct 15 2015 04:59am

I'm gonna say 69