Even if your balance does average to $100 over time, this is good practice for deciding on a strategy and sticking with it, despite what your emotions will tell you.
Well... not trading at all is a strategy too, if you look at it that way. I expect I won't be able to outperform that one in the long term.
the trading system is simply a vehicle to give you a positive mathematical expectation on which to use money management.
You need to get your money management correct. Let's say we do a coin toss and every time it lands on heads I give you $2 but every time it lands on tails you give me $1. Your expected value per coin toss is $0.50, but your optimal bet is not $1, it is 25% of the money you are willing to trade with. So if you started with $1 then you would bet $0.25 each time.
So for this example the optimal f is 0.25. For this example the equation is:
f = ( ( b +1 ) * p - 1 ) / b
f = the optimal fixed fraction
b = the ratio of amount won on a winning bet to the amount lost on a losing bet
p = the probability of winning the betDoing some backtesting you see that the player before you had a win and loss string of:
-1, +2, -1, +2, -1, +2, -1, +2, -1, +2
10 bets, 5 winning, 5 losing or a total of $10 won and $5 lost. If you originally bet $1 then you would have made a 90% return.
Here,
b = $10 / $5 = 2
p = 0.5
so,
f = ( ( 2 + 1 ) * 0.5 - 1 ) / 2 = 0.25What this f value means is that if you bet 0.25 of your total stake then you will leave with the optimal amount of winnings. So for example if you only had $1 your optimal bet is $0.25. If you had $10 your optimal bet is $4. If you bet too much, for example your whole stake of $1 then you could quickly lose all your money and can't bet anymore. If you bet too little then you don't win enough money to make up for the times you lose.
For your flipist strategy, you won't have only two outcomes. You can lose or win any amount of money. So the equation is a little more complicated and you need to do backtesting. The backtesting will show if there is a positive expectation to your strategy. If there is no a positive expectation then no type of money management will help you win money. It is like those people that go to the casino and think their "system" works. In a casino they have a negative expectation of winning so nothing they can do, besides not gambling, will lead to a positive expectation.
Then with that positive expectation you are able to see which f is optimal. You run the equation below with f in a range from 0.01 to 1 and see where the geometric mean reaches its peak.
G = { Sum( 1 + f * (- Trade i / Biggest Loss ) ) } ^ (1/N)
- Trade i is the profit or loss (with the sign reversed) on the ith trade
Biggest loss is a negative number of the largest drawdown
N is the total number of tradesWith your current strategy you are making 3 decisions.
1) you flip a coin and based on the flip you buy, sell, or do nothing.
2) you decided how much to risk
3) you decided to reinvest any profits