When to Convert my Dollarses into Euroses

I sell Poker Copilot for US$49.95. People pay in US dollars. Because I live in Germany, my landlord, my supermarket, and my local Apple store all want to be paid in Euros. Therefore I must decide when to bring money from my US-dollar-denominated account into Germany.

Now I could speculate on where the USD/EUR exchange rate is headed. I could try to guess the ideal time to convert the money. But that's a mug's game. Even those who make their living from exchange rate speculation don't do very well from it, on average. Yes, yes, I know about your cousin/friend/hot-shot analyst who made a fortune from exchange rate speculation. According to probability some people will get it right sometimes. A few people will get it right many times. These people are luckier than they realise.

Consider this contrived story: 1296 men go to a casino, each with $100. They all play on the same roulette table at the same time. 36 of the men put their entire $100 on number 1. Another 36 put their money on number 2. And so on, so that each number has $3600 staked on it. The wheel spins. Lucky number 7 comes up, of course. 1260 men leave sullenly, and never talk about their gamble and subsequent loss.

But 36 men have now 36 times the amount of money they started with: $3600 each. Feeling like they've got this roulette game figured out, they bet on another spin of the wheel. The first man bets his $3600 on number 1, the second man on number 2, and so on. The wheel spins. The result is 11, as a wise person would expect. Another 35 men leave disheartened and go back to their normal jobs as accountants, hairdressers, and delivery drivers.

But one man, one lone man now has $129,600. He is celebrated as a champion gambler, almost divine in his ability to guess right. He writes a popular book, "I Won...and So Can You!". It outlines his theory on picking subsequent prime numbers for guaranteed success. People use him as an example to prove that you can make a good living playing roulette. But he is not divine; he is fooled by randomness. So too are his many followers. He actually made terrible decisions, but got very, very lucky.

It's easy to get fooled by similar successes in currency speculation, because we ignore (or don't here from) the losers. There's ample research showing that a random number generator is as good a predictor of exchange rate movements as the typical analyst.

So back to my problem: What's my solution to the "I don't want to be a speculator" problem? When do I move my money from USD dollars to Euros? As often as possible while not incurring too many fees. Once per month. Sometimes I'll get a good rate, sometimes I'll get a lousy rate. But over the course of time, the good and the bad will average out and I'll end up with a reasonable rate over all.