Variance Is Your Friend

One of my first trips to Las Vegas after I turned 21 was with a few software engineer friends. These were sharp guys with degrees from elite universities and already considerable career accomplishments.

We played some red chip blackjack. None of us was trying to get an edge at the game, though I knew basic strategy. We played for a while, and then my friend got a blackjack—except the dealer had an ace. When this happens, the dealer offers you a guaranteed even money payoff on your hand. If you turn it down, then if the dealer has a ten-card in the hole, you push, and if not, you win 3-to-2. (This was back in the old days when blackjacks still paid 3-to-2.)

This offer is exactly equivalent to the insurance bet the dealer offers every time she shows an ace. You bet half your bet that the dealer has a ten-card, and if you’re right, the insurance bet pays 2-to-1. It’s a bad bet, since only 4/13 of the cards in the shoe are ten-cards, so fair odds would be 9-to-4 instead of 8-to-4 (or 2-to-1).

My friend took the even money. Afterward, I explained why it was a sucker play. The simple math involved was well within his competency. But he said that he would rather just lock in the win than gamble.

For the rest of the evening, my friend took every offer of even money. He rejected the insurance bet every other time it was offered (i.e., when he didn’t have a blackjack). I asked him why he would reject the mathematically identical insurance bet when didn’t have a blackjack. He explained that he could lose the insurance bet and then go on to lose the hand as well, which would be a total loss of a bet-and-a-half. Insurance just felt like extra risk to him most of the time, but when he held a blackjack, it felt like he was “locking in a win.”

Why has this memory stuck with me through the years? My friend was trying to avoid variance. I’ve always thought it very odd that people come to casinos to gamble voluntarily at a disadvantage—yet once they’re there, they often take additionally the worst of it to eliminate the variance. Far from locking in a win, this strategy locks in the loss.

People do it with sports parlays also. They bet eight games, and then if they win the first seven, they try to hedge away the risk of the final game to lock in a win. But usually they have to pay vig to hedge the last game, and they would have been better off just not adding that eighth game to the parlay in the first place. Since there’s no scenario where they’d win the first seven games and still want to have action on the eighth, why on earth did they bet that game in the first place?

I think it’s human nature. We humans just seem to dislike variance—at least certain types of variance, and at least most of us. I see this variance-avoiding behavior all the time. Not just from casual gamblers like my engineer friend or the occasional parlay player, but from would-be professionals.

Here’s the problem. The only reason that edge exists in the first place is because of the variance. Edge without variance is farcical. No one will sit there and hand you money wager after wager without wising up quick.

I remember about ten years ago when online casino bonus hunting was a big thing, many of the people scrounging the bonuses devised strategies to complete the wagering requirements with the least variance possible. They would bet every number simultaneously on a roulette wheel or both the pass and don’t pass line on a craps table.

This behavior throws up a huge red flag for the counterparty, however. No one is going to sit there and let you bet both sides over and over again—and watch you win—and let you keep doing it for long. If you want edges, and you want them to last, you have to embrace the variance.

More often, however, attempts to reduce variance don’t just get you backed off. They cut substantially into your edge until you may no longer have an edge at all.

This is what’s happening in $2-$5 no-limit games across the country. For whatever reason, the regulars at this level of the game tend to be highly variance-avoiding. Their worst nightmare is to flop a hand, call three streets with it including an all-in on the end, and find out that they were behind the whole way. They say things like, “I’ll wait for a better spot,” or, “I’d rather lose a small pot than a big one,” to justify this behavior.

Unfortunately, no-limit hold’em doesn’t let you get away with this. Any strategy you choose with the goal of reducing variance has a natural counter-strategy. For these $2-$5 players who don’t want to call off stacks, the counter-strategy is obvious—you just build pots with them and then bet all-in on the river. They won’t call. They’d rather lock in a smaller loss than gamble for all the money.

Sometimes this refusal to pay off is a rational adjustment to the strategies of the other players in the game. But I can’t tell you how many times I’ve put out that river bet and had someone stare me down and say, “I know you’re bluffing almost every time, but I just can’t gamble with you.”

The desire to lock in small loses to avoid big ones is utterly self-defeating, both in no-limit hold’em and in many other areas.

Final Thoughts

Variance is your friend. Variance is where the edges live. Nearly always, if you remove the variance from a game, you’ve also removed your edge. (And if you haven’t removed the edge, it will disappear soon enough, because people won’t let you profit without risk for long.)

In no-limit hold’em, don’t alter your strategy in an effort to reduce your variance. You will nearly always reduce your winrate significantly at the same time. It’s no coincidence that some of the most successful poker players are also commonly characterized as “fearless.”

Furthermore, when a new opportunity in gaming, business, or life comes along, don’t always latch onto the lowest variance strategy first. The more you go into risk-management mode from the get-go, the more likely you are to miss the very best opportunities of all. ♠

Ed’s newest book, The Course: Serious Hold ‘Em Strategy For Smart Players is available now at his website edmillerpoker.com. You can also find original articles and instructional videos by Ed at the training site redchippoker.com.