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Fluctuations In Variance Can Make Or Break You

By Jerry “Stickman” Stich


Variance is a component of any casino game. By variance I mean fluctuations in the gaming bankroll. There are periods where the player wins more that he loses. There are periods where the player loses more than he wins and there are periods where the player stays basically even. These periods can vary in length and cannot be predicted. Each video poker game and pay schedule has its own variance and return percentages. The bankroll will vary with time, but the more hands played the closer the players loss (or in very rare cases the win) will be to the mathematical return of the game.

While I enjoy the upswings of variance, I totally abhor the downswings. When choosing a video poker game I prefer those with a low variance. I normally play single-play video poker—those that play only one hand per game. Since it is a fact that the more hands you play the closer to the mathematical average you become, does it make sense for a variance- averse player to switch to a multiple-play game? There are games that play three, five, 10, 50 and even 100 games at a time. I normally play dollar single-play, risking five dollars a hand. What if I were to play the same amount per hand on a one cent 100-play game? Would my variance go down?

Multiple-play games deal the exact same hand to three, five, 10, 50, or 100 hands. The player then decides which cards to save for all the hands dealt. The strategy for playing a multi-play game is exactly the same as when playing a single-play game.

If you are dealt a good initial hand you can make a lot of money. Imagine your delight at being dealt four-of-a-kind! However if you are dealt a poor hand, you stand to lose a lot of money. Over half of all hands in video poker end up being losers. Because of this, the variance (amount of bankroll swings both plus and minus) for multiple-play games is higher than for single-play games. You need a bigger bankroll to play multi-play games of the same denomination.

In a single-play game, variance is higher when more money is paid out on high paying hands. For example, 9/6 Jacks or Better (where a full house is paid at 9-for-1 and a flush is paid at 6-for-1) has only one very high paying hand—the royal flush. The variance on this game is 19.5. Bonus Poker is different than Jacks or Better because it pays a bonus for four aces (80-for- 1 instead of 25-for-1) and four 2s, 3s or 4s (40-for-1). Payoffs for a full house and a flush are reduced to make up for the higher payoffs on the quads. The variance for Bonus Poker is 20.9—a seven percent increase over Jacks or Better. Double Bonus Poker increases the bonus on four aces to 160-for-1, the bonus on four 2s, 3s, or 4s to 80- for-1, and the bonus on 5s through kings to 50-for-1. Two pair payoff is reduced to 1-for-1 to compensate for the increased quad payoffs. By concentrating much more of the payoff money in fewer, large payoffs and reducing the more frequent lower payoffs, variance on Double Bonus Poker soars to nearly 28.3 – a 48 percent increase from Jacks or Better.

In multiple-play games, variance increases as the number of plays increase—not because more money is concentrated in fewer high paying hands, but because the strength of each multiple- play game is determined by the initial five cards that are dealt. If it is a strong hand, each play will have a strong hand. If it is a weak hand, each play will be weak. For example, if the initial hand contains three aces, the minimum each play will return is 3-for-1. If however the initial hand contains nothing and needs to be completely discarded, the chances for a positive outcome for this hand are small.

Now let’s look at some specific games, plays and variances.

As stated above, variance for single-play Jacks or Better is 19.5. A 3-play Jacks or Better game has a variance of 23.4 – a 20 percent increase. In the 5-play version of Jacks or Better the variance now becomes 27.3 – 40 percent greater than single-play. 50-play Jacks or Better has a variance of 115.8, and the 100- play version has a variance of 214 – a whopping 997 percent greater than the single-play version of the game. That is quite a variance for a game that initially has a relatively low variance.

What about a game with a higher single- play variance? Double Bonus Poker has a single-play variance of 28.3 – 48 percent higher than single-play Jacks or Better. The 3- play version of Double Bonus Poker has a variance of 35.0 – a 24 percent increase from the single-play version. 5-play Double Bonus Poker has a variance of 41.8 – 48 percent higher. The variance on 10-play is 58.5 – 108 percent higher. 50-play variance is 194.4 – 588 percent higher. And 100-play variance is 364 – 1188 percent higher!

Those are some pretty big numbers. But what do they mean to you, the average video poker player?

The more knowledge you have about the game you are playing, the better prepared you are to enjoy the game. If you are planning to play multiple-play video poker you will need to bring a larger bankroll in order to play as long as could on a single-play game. Even on the relatively low variance Jacks or Better, the variance of the 100-play game is 10 times that of the single play game. This means that even if you were to play a lower denomination multiple- play version of the game you still may need a larger bankroll.

For example, if you normally play single-play Jacks or Better at the $1 level, it may seem logical that you could play 100-play Jacks or Better at the 1C level. After all you wager five dollars on each hand in either game. But, by looking at the increased variance for 100-play (10 times that of single-play), it is easy to see that the same bankroll will not nearly be enough. Rather than smoothing the ups and downs, multiple-play games increase the ups and downs.

Keep in mind that variance can be good or bad. When riding the wave of positive variance, life is very good indeed. However, when wallowing in the pit of negative variance, life is very tough. If you are variance averse, multiple-play video poker is not for you. However, if you do want to try your hand at multiple-play, it is a good idea to make sure you have a large enough bankroll when you gamble. Keep your casino experiences enjoyable. Make sure you bring a large enough bankroll with you if you are planning to play multiple-play video poker.

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