I thought of a stock trading strategy: buy 5/10 of what you want, then set good-until-cancelled orders to buy 1/10 more if it goes down 5% or sell 1/10 if it goes up 5%. If the stock oscillates you make money. If it goes down, when it has dropped 21.6% you've bought all you intended to, or if it goes up 27% you've sold your original half at a 16% gain (an 8% gain for your total money).

But is 5% the right amount? Going up 5% then going down 5% would gain you 0.5% of your investment, or 0.25% of your total, it's a 0.125% gain per trade. If you did 10% instead of 5%, up and down is 1% of your investment, 0.5% of your total, so 0.25% gain per trade. So 10% is better per trade than 5%.

But wait, there's at least twice as many 5% trades as 10% trades. In fact, there's usually about 3x as many 5% trades as 10% trades (from surveying various stocks this year and last). So 5% is better than 10%, and 2% is better than 5%, and 1% is better than 2% ...

But wait, 10% buys all you intended at 37.9% down instead of 21.6%, and sells everything by 61% up instead of 27% up. In order for 5% to have the same trading range, you'd have to trade in increments of 1/20th instead of 1/10th. Then 5% earns 1/4th as much per trade as 10%, and there are only 3x as many 5% trades as 10% strades, so 10% is better. And 20% is better than 10%, and 50% is better than 20%, and 100% is better than 50% ...

But wait, ...