A constant risk trading strategy in the day-trading context is where your maximum loss possible is a constant. There are other definitions in trend-following etc contexts where you choose a position size so that the typical or expected daily movement up or down is a constant over time and markets.
Using the first definition, once you choose a stop loss, you compute the loss per contract or share if the stop was triggered and divide the fixed maximum loss figure by that to find out how many contracts or shares to buy. For example, if you are willing to risk $2000 on a trade and a contract will lose $1000 in the worst case, you buy (or sell) two contracts.
The reason this works is the maximum downside loss is capped but by trading more contracts when possible the upside is increased. This helps create asymmetry.
This graph shows possible loss on the x-axis and trading results (in backtest) on the y-axis, when trading one SPI contract over the last 13 months:
And this is what happens to the returns when the maximum loss is set at the average $2,300 (yes the stop loss can occasionally be exceeded when the opening price of the day is above the entry stop):
This has a lower information ratio (similar to Sharpe ratio but without deducting the risk free rate) than the one contract strategy though. It misses out on really big gains when volatility is high. But if you combine the two and set a minimum maximum loss at $2,300 you get better results than either strategy alone. Below $2,300 potential loss you trade a variable number of contracts and above it one contract only:
This has a higher information ratio than either simple strategy but it does take on a lot more risk at times than the constant risk strategy, which for a small account trading full size futures contracts could mean just not trading when volatility is high.