Brain teaser 2: Who made the most?

There are 6 traders. Each of them has a risk reward of 1:1 but different position sizing and win%. Who make the most money after 100 trades if they are compounding on each trade? Please rank them according to their final capital.

Trader A: Win% = 55%, Position size = 25% of capital.
Trader B: Win% = 55%, Position size = 15% of capital.
Trader C: Win% = 60%, Position size = 40% of capital.
Trader D: Win% = 60%, Position size = 50% of capital.
Trader E: Win% = 65%, Position size = 2% of capital.
Trader F: Win% = 65%, Position size = 1% of capital.

Please do not show your calculation here because the solution is very easy.

Trader d.

The results, ranked by % of starting capital are:

E: 179%
B: 145%
F: 134%
C: 78%
A: 51%
D: 3%

With variance it could be any of them. Without variance, trader E. The first four are overbetting, while the latter two lack the balls make the most of their high winrate. None are impressive.

My results are the same as capitalist88's.

According to the Kelly formula, the optimum wager size for each trader is as follows:
A: 10%
B: 10%
C: 20%
D: 20%
E: 30%
F: 30%

In which case, the ending balances would be (as a % of original capital):
A: 165%
B: 165%
C: 749%
D: 749%
E: 9655%
F: 9655%

Of course none of this takes risk of ruin into account.
Does anyone know the formula for calculating the risk of ruin within the 100 trades?

my head hurts now.. Suck at math.

huuu all the above?

I agree with capitalist88.

hanover: "Of course none of this takes risk of ruin into account."
There is no probability of ruin here; with the compounding, account might become tiny, but never zero. That's actually one of the main points of Kelly's formulation, no?

Mr J: "With variance it could be any of them."
Okay, so where's the formula for the standard deviation? And after you get it, what's the probability that the ballsy Mr B beats the wossey Mr E?

This excercise can be beneficial under the hypothetical scenario that the win ratios are held constant. They can be useful for basic money management on a smale scale. However, random walk hypothesis makes completely accurate predictions impossible. It is my belief that a great trader knows how to determine probabilities and knows how to manage them.

http://en.wikipedia.org/wiki/Random_walk_hypothesis

Well I guess this is too easy for most people here.

Use binomial distribution.