Forex Probability, Expected Value, & High-Risk Trading

Suppose a friend comes to you with a proposition:

"Here is a regular six-sided die. You put up $25 to roll a minimum of 5 times. If you roll a 1 thru 4, I double your money. If you roll a 5 or a 6, I keep your $25. You can play till you win 5 in a row or you are broke."

Would you take the offer?

The probability of rolling a 1 thru 4 is approximately 67%. The probability of doing it 5 times in a row is... 4/6 x 4/6 x 4/6 x 4/6 x 4/6 = .1316 = 13%

The expected value of such a proposition is... (.13 x $800) + (.87 x -$25) = $82.25

So statistically speaking, this is a winning proposition. Now, let's apply it to trading.

Trader A has $800 to start with. Assuming he is a good trader, a 67% win rate is reasonable. Also, assume a somewhat conventional MM approach where that trader earns a very respectable 10% a month. After 1 year, Trader A would have $2,510 in their account.

Trader B also has $800 to start and also wins at a 67% rate. Assuming he has access to a high-leverage broker (say 1000:1), he can in theory double his account balance with a somewhat small market movement (say 10-20 pips). He chooses only to deposit $25, and takes the approach from our dice game. He will have a total of 32 deposits before he is broke. Say he goes a month or so and has yet to win 5 in a row. He has deposited 8 different times and is down to $600. Then, he finally wins 5 in a row, taking his total to $1,400 after, say, 6 weeks time. Then, he starts the process again, now with $40. He has 35 total deposits. Assume once again, he loses 8 times. Now he's down to $1,080. Then he wins 5 in a row taking his total to $2,360. So, in 3 months time he has made nearly what Trader A made in an entire year.

The "X factor", of course, is statistical variance. How long will it actually take someone with a 67% win rate to cash in on that 13% likelihood? He may go on a favorable stretch and take his account to five figures in just a couple months. He may burn through all 32 deposits of $25 without ever hitting 5 in a row. The question is... Is it reasonable to think that Trader B can be far more successful than Trader A?

Source.