Low- and high-variance video poker

24 September 2015

By John Grochowski

Experienced video poker players know to check pay tables before they play, and to pay special attention to the returns on full houses and flushes.

On a recent casino visit, I found 25-cent Double Double Bonus Poker with 9/6, 9/5 and 8/5 pay tables on the same slot floor. The best version, the one that pays 9-for-1 on full houses and 6-for-1 on flushes, returns an average of 99% with expert play, while the 9/5 game pays 97.8% and the 8/5 version returns only 96.8%.

A little comparison shopping before playing allowed me to choose the best game. Shopping around also includes comparing different games, and there are factors beyond payback percentage. There’s also variance and your bankroll to take into account.

Variance basically tells us how much your short-term results are likely to vary from the game’s long-term expected return. If every player makes optimal plays, then over millions of hands, 9/6 Double Double Bonus is expected to return 98.98%, which we round up to 99.

However, you won’t get precisely 98.98% every time you play. Rare, big-paying hands such as royal flushes (4,000 coin return for a five-coin bet) and four aces with a low-card kicker (2,000 coins per five wagered) will turn some sessions into big winners. In some sessions, even moderate wins such as full houses and flushes will seem out of reach, and tiny returns will send you fleeing.

Double Double Bonus is a high-variance game because much of its overall payback is tied up in uncommon hands, especially quads. Given a five-coin wager, most quads in Double Double Bonus return 250 coins, with 400-coin pays on four 2s, 3s or 4s and 800 on four aces. That’s kicked up to 800 coins when four 2s, 3s or 4s are accompanied by an ace, 2, 3 or 4, and 2,000 on four Aces when the fifth card is a 2, 3 or 4.

Compare that to Jacks or Better, a low-variance game. All quads return 125 coins for a five-coin bet. The tradeoff is that on Jacks or Better, you get a 2-for-1 payback on two pairs – a much more common hand than four of a kind – while Double Double Bonus returns only 1-for-1.
The 9/6 versions of the games have similar payback percentages, with 99.5% on JB and 99% on DDB. But much more of the payback on DDB is concentrated into rarer hands. That leads to a high-variance game, and we can quantify that. The variance for 9/6 DDB is 30.78, much higher than the variance on 9/6 JB, which stands at 19.51. In their 8/5 versions, variance is 19.32 on Jacks or Better, a 97.3% game, and 32.40 on DDB.

Other high-variance games include Bonus Poker Deluxe (32.13 in its 9/6, 99.6% version, 31.96 at 8/6, 98.5%) and Double Bonus Poker (28.26 in at full-pay 10/7/5, 100.2% with expert play, and 28.55 at 9/6/5, 97.8%).

On the low-variance side is Bonus Poker (20.90 at 8/5, 99.2% with expert play; 22.78 at 7/5, 98.0%).

Where all that makes a difference to you is in the playing experience. Are you short-bankrolled, looking for a game that has the best chance of extending your play? Then you want a low-variance game. Are you looking for games with more chances at a big payoff, with the tradeoff being that they can deplete your bankroll rapidly? Then look at the high-variance games.

Look for John Grochowski on Facebook (http://tinyurl.com/7lzdt44) and Twitter (@GrochowskiJ).