Leverage has counteracting forces: It either amplifies your gain or amplifies your loss. Almost everyone understands that.

But not everyone understands how these counteracting forces come into play when applied over longer time periods and through multiple bets, even as these bets have positive expected returns.

To explain, let’s take an example.

Say you have a rigged coin-tossing game in which the coin is designed so that it lands on heads 51% of the time and lands on tails 49% of the time. The payoff is even. You are well aware of the coin’s design and you know that the probabilities are in your favor. You now also know that you must bet bankroll proportions to avoid gambler’s ruin.

Let’s first see what might happen to your wealth over time if you continuously bet 1%, 2%, or 5% of your bankroll on heads 1,000 times.

With a 1% betting strategy, the simulation shows that you could have made a return of 47.7% of your original bankroll with mild volatility. You could also have made a higher return, albeit more volatile, with larger bet sizes. This is the intuitive way to think about leverage.

Now, let’s look at the counter-intuitive reality of what happens when we increase your bet size even more, say to 10%, 15%, or 30% of the bankroll with each bet.

As our simulation shows, it’s easy to lose money, even with a mathematical advantage. Increasing your bet sizes too much will devastate your bankroll: With a 10% betting strategy, you would only have half of your bankroll left, and with 15% and 30%, your bankroll would essentially be ruined.

Think about what’s going on for a minute. With a 5% bet size or 2% bet size (which, as we’ll later find, is the long-run optimal), your bankroll would increase faster than a 1% bet size. But with a 30% bet size, it would lead to fast ruin. In the first case, leverage is obviously helping, and in the second case, it’s detrimental.

Why is that?

The reason is that at a very specific point, the marginal profit you earn from adding more leverage shrinks and eventually turns negative. To further explain, let’s switch our example around to an equal probability bet but with unequal payoffs and which requires actual leverage in the terms of borrowed money.

Say you have an investment opportunity that is 50% likely to work out. If it does, you will earn a 20% return on your investment, and if it doesn’t, you will lose 10% of your investment. The payoff ratio is therefore 2-for-1 and the reason why we can now borrow money to amplify our return is that risking 100% of our capital can only lead to a loss of 10%.

Now, instead of doing a 1,000-bet simulation, let’s only do two successive bets: one win and one loss (the order doesn’t matter). Then we can iterate using different levels of leverage.

What we see is that as soon as the leverage exceeds 2.5x, the return made from the two bets starts to drop off and eventually goes negative at over 5x leverage.

The reason why this happens is that the loss incurred on the second bet more than offsets the return made on the first since that loss is taken from a larger pool of capital. It’s the same geometric effect as if you gain 10% on an investment and then lose 10%, you’re one percent down on your original investment.