# Variance is Desirable On its own, variance is not a bad thing. As gamblers, investors, and risk takers, it’s a fallacy to always seek lower variance. In fact, many gamblers, professionals and recreational alike, enjoy variance. **Variance is the underlying asset of gambling**, for losers and winners alike. For a bettor who knows he has an edge and has a proven strategy to realize that edge over the long term, **extra variance should be treated as an asset**, not a liability. (I’ll discuss this point further in a future post.) It’s not because we can’t stomach the variance. Actually, variance is critically important to long-term profitability in gambling. Without variance, losers would never win, winners would never lose. The losers would stop gambling — and stop losing. The winners would be too easy to identify — and nobody would gamble with them. The more variance we’re able to handle, the better we’ll be able to sustain an advantage over the long term. But “handling variance” in this case isn’t about emotional control or risk aversion. > **The problem with variance is that it prevents us from knowing what we need to know.** In particular, variance prevents us from knowing what our edge actually is — or if we have an edge at all. In the first plot above, how many bettors, after losing 80% of their bankroll almost immediately, would continue betting as if nothing was wrong? At that point, it’s natural to question whether the underlying assumptions are accurate. It may be prudent to quit altogether, but variance prevents us from knowing for sure. The need learn and update on the fly — and to quit before it’s too late — is the primary reason to limit variance (but not too much). Variance is too much if it prevents us from figuring out what we need to figure out before it’s too late. What exactly this means varies depending on what we need to figure out and how much we’re willing to risk in order to find it out. We bet in order to realize our estimated advantage, and we track results in order to confirm that our estimated advantage is an actual advantage (i.e., that our [expected value is actually value expected](https://harrycrane.substack.com/p/expected-value-and-value-expected)). To do this systematically it’s beneficial to think about which situation would need to occur in the short term in order for us to rethink our advantage, and to *set up a strategy so that if that situation does occur then we actually do have enough evidence to stop betting*. To answer this, we compute the probability of experiencing a loss of 50% or more during the first 1,000 rounds of Kelly betting if our edge is correctly estimated at 10%. We find that this probability is approximately 46%. In other words, it’s not very unlikely at all. The point of computing these probabilities is _not_ to calculate the probability that we do or don’t have an edge — that is not what these probabilities mean — but rather to devise a strategy that allows us to learn about our true edge at a rate we’re comfortable, and to be decisive about quitting once we’ve gained sufficient evidence. > Variance is too much if we are very likely to end up in an uncomfortable situation and not know whether we should quit or keep going. --- Date: 20240502 Links to: Tags: References: * [How much to bet? - Harry Crane](https://harrycrane.substack.com/p/two-arguments-for-fractional-kelly)