Size DOES Matter (snicker) Taking Down the Martingale Part II

In today’s post, I show you how to take a winning game and become a loser at it. How? Because it IS possible to set up one’s trading with an edge that’s hard to beat… unless you beat it yourself. “We have met the enemy,” Pogo says, “and he is us.”

Of course, I don’t want to show you how to lose money so that you go out and DO it… I’m showing you how it’s possible to lose money at a winning game in order to expose another flaw in most folk’s trading plan. And help you fix said flaw. Cool? Let’s get started!

In Part I, we looked at the formula for calculating expectancy:

E = [P x W] – [(1-P) x L]


E is ‘Expectancy’ or Expected Return per Play
P is Probability of winning, expressed as a fraction
W is Amount of a Win
L is Amount of a Loss

A trading coach named Ralph Vince did a remarkable experiment. He rounded up 40 Ph.D’s… ruling out those whose degrees were in probability and statistics. In other words, really really smart folks that didn’t fully understand the implications of the above equation. He gave them a winning game: an even money wager with a 60% probability of winning. They all had $1,000 in ‘virtual’ dollars to begin with, were given 100 trials in which to bet, and were given total latitude as to how much to wager. They were prescribed no system for sizing their bets….

Wanna be shocked? 95% of the Ph.D’s  LOST money.

Only two out of the forty players were able to beat a very beatable game: 60% of the time, players would win on an even-money bet. But most of them still couldn’t make it work. Let’s plug in the numbers:

E = (.6 X $1) – (.4 X $1) or .20 cents for every dollar wagered. (Hey, didja get all that? It’s 60% probability of a win, only as a fraction: .6, TIMES a dollar, MINUS the probability of a loss times a dollar. SO for every dollar you bet, you can ‘expect’ that over time your winnings will equal .20 cents per dollar you bet.

So HOW did 38 out of 40 Ph.D’s LOSE at this game?

Well, hmm. What if you bet your whole $1,000 on the first trial, and lost. Sure, you would have a 60% chance of winning on the next try but there wouldn’t BE a next try… you’re broke.

What about being too conservative? If you only bet $1, and did it 100 times… that’s $100 wagered at a .20 cent expectancy. You’ll end up with around $20 bucks to add to your original $1000 bankroll (yawn), a .2% gain in a game that SHOULD have made you some serious bank.

What if you were too conservative at first, but then stepped up your play a little late in the game? Say you bet only $5 of your $1,000 for the first 90 trials? Then you could expect to be ahead by around  $450 X .20 cents = $90 bucks. With $1090 in your stack and only 10 tries left you figure that it’s time to risk more. You bet $300 once, lose it, get discouraged because you are at $790. Now you bet a more conservative $100 for each of the remaining 9 tries. You win five times, lose three… so you’re at $990 with one try left. And that try has a 60% chance of winning, regardless of what you wager.

In the above scenario you made only ONE foolishly high wager, bet conservatively the rest of the time, and it still comes down to just one more roll of the dice to see whether you win or lose a very, VERY beatable game. Wow.

Yikes… this is the inevitable outcome of NOT running the numbers. When you size your bets without a system, and bet according to what you feel instead of what’s ideal… you will lose.

Let’s take the above scenario again and think it through: Wagering too MUCH can cause a problem for obvious reasons… because though probability is 60% for each trial, streaks of wins and losses WILL happen. It’s not unthinkable that you would get three winners or three losers in a row. So betting a third of one’s account would be exceedingly unwise.

Betting too LITTLE will result in failure as well, though that failure would not be a problem of losing but of not gaining what should be coming as a result of a disciplined trading plan.

This is why I say that SIZE MATTERS… because it does. Bet size, that is… called ‘position sizing’ by trading coach Van Tharp. Of all the different factors of a trading system, these two are most important: positive expectancy (quantifying probability and payout for a trading edge) and a solid money management strategy.

With an amount of only $1000 to trade with and a system like the one above with which to trade, how about a bet of $100, times 100? That would be a total amount of $10,000 wagered. 60 wins equals $6000 in, 40 losses equals $4000 out, for a total of $2000 earned from playing a bankroll of $1000. Of course, if one had ten losses in a row to begin, this bet sizing plan would not work. But the likelihood of that happening is quite low with a 60% chance of winning every time.

The trick is finding a system with that kind of positive expectancy, AND matching the bet sizing to it appropriately.

For the answer we’ve got to go to Bell laboratories in the 1950’s, to some very interesting gentlemen and the beginnings of what is now called game theory. In the next post we’ll talk about some great names in the world of finance, mathematics, and information. Some of these names you may have never heard… but they have shaped our world and a lot of what goes on behind the scenes.

Okay Traders! Post away… We’ve gotten a lot of attention from the “Google Slap” post but now things have settled down a bit. I’m anxious to hear from you.

Happy Trading,


About Kurt Frankenberg

Kurt Frankenberg is an author and speaker about entrepreneurship, martial arts, and trading the stock and options markets. One of several "Biznesses" he founded as a teen, The Freedom School of Martial Arts, has been in continuous operation since 1986. Kurt lives in Colorado Springs with his wife Sabrina, German Shepherd Jovi, and his ninja cat Tabi.