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Don't ignore variance in setting video poker bankroll

Don't ignore variance in setting video poker bankroll

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Payback percentage tells us much of what we need to know in comparing video poker games, but it doesn’t tell us everything.

There’s also volatility to consider, and that can be measured in variance. Given a large number of sessions using expert strategies, what portion will bring larger than average wins? What portion will bring larger than average losses?

Those things go together. Double Double Bonus Poker, with its big four-of-a-kind jackpots but only 1-for-1 pays on two pairs, brings a larger than average share of big wins but also a larger than average share of bankroll-busting fast losses. Jacks or Better, with small quad pays but 2-for-1 pays on two pairs, will have fewer big wins, fewer big losses, and more sessions closer to average results.

You can put a number on that through variance. Low-variance games include Jacks or Better (19.51 variance with a 9-6 pay table; 19.32 on 8-5), and Bonus Poker (20.90 at 8-5; 22.78 at 7-5).

Both pay 2-for-1 on two pairs. The effect of concentrating more of the overall return in such a common hand is to smooth out results. There are fewer big wins, and fewer fast bankroll drains.

Most other non-wild card games pay only 1-for-1 on two pairs while increasing pays on quads. That results in higher variance on games including Bonus Poker Deluxe (32.13 at 9-6; 31.96 at 8-6) and Double Double Bonus Poker (30.78 at 9-6; 32.40 at 8-5).

As a practical matter, players need to think about volatility or variance when they think about bankroll for the games they play.

A game with high variance may require a bigger bankroll for a fighting chance to stay in the game even if it has a payback percentage as high or higher than a lower variance game.

Let’s look at two games with similar payback percentages. With expert play, 8-5 Bonus Poker returns 99.17 percent and 9-6 Double Double Bonus return 98.98 percent. Making max-coin bets of $1.25 on quarter machines and playing optimal strategy at an easy pace of 500 hands an hour, the average loss per hour comes to $5.19 on 8-5 BP and $6.38 on 9-6 DDB.

The way they get to those averages is dramatically different with more return on common hands in B and more on the rarer quads in DDB.

Accordingly, bankroll requirements are very different. Planning to play quarter machines 10 hours with a chance of busting out of 5 percent or less takes $510 on 8-5 Bonus Poker, but $885 on 9-6 Double Double Bonus.

Bankroll requirements can be lower on lower-playing games that have less variance. Take 8-5 Jacks or Better, a 97.3-percent game with expert play. At 500 hands per hour, average losses with expert play come to $16.88 on q quarter machine.

In 9-6 Bonus Poker Deluxe, the return is higher at 99.64 percent and the average loss per hour lower at $2.25. Yet the bankroll needed for a 5 percent or less chance of busting out within 10 hours is $770 on 9-6 BPD and only $570 on 8-5 JB.

You’re a lot more likely to win big on Bonus Deluxe. It pays 400 coins for a five-coin wager if you get any four of a kind compared to only 125 on Jacks or Better. But because of the 1-for-1 return on two pairs, you’re also a lot more likely to churn through cash fast on BPD.

The attraction of higher variance games is obvious. We all like a chance to win big. But fast losses happen too, and you need to be prepared.

Look for John Grochowski on Facebook and Twitter (@GrochowskiJ).

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