As far as casino gambling goes, blackjack is one of the better games to play. Your chances of winning any given hand are fairly decent: Less than–though not much less than–50%.

However, because your chance of winning a hand is less than 50%, the more hands you play, the less chance you have of coming out ahead in the end.

Mutual funds work the same way.

Study after study has shown that the higher the operating costs of a fund, the worse its chances of beating the relevant index in any given year. This shouldn’t really come as any surprise. For every additional percentage of operating costs, the fund managers must outperform the market by 1% in order to justify the use of their fund over an index fund.

Of course, not every manager can succeed because, for every dollar that outperforms the market, there’s a dollar underperforming by an equal amount. So (prior to considering costs) half of all dollars in non-index funds outperform the market, and the other half underperform. Therefore, when looking at after-cost returns, we must conclude that greater than half of all non-index-fund-dollars will underperform the market each year.

So if your probability of outperforming an index fund is less than 50% each year, what are your chances of outperforming over a multiple-decade period? It’s rather like playing 30 hands of blackjack and expecting to come out ahead, isn’t it?

Takeaway: If you’re going to invest in actively-managed funds, make darned sure they’re low-cost ones.