Some time ago, I did a column which I called "Taking a Shot" wherein I related an experience I had while at a local casino with a friend. In it, I told how we decided to risk a few hundred bucks in an effort to 'get lucky' and grab a big progressive Royal Flush. No, we didn't get it, but the object of that column was to demonstrate how difficult it is to pursue such jackpots with a limited bankroll. If you read that article (it's in the archives of the "Video Poker Bible"), you'll see that I made some assumptions about different Video Poker games, especially those like Jacks or Better, which pays 10 for 5 on a hand of two-pair and those which pay only 'even-money' for that hand, like Double Bonus poker. As I was analyzing some progressive games which I've been playing lately, I discovered that some of my assumptions were wrong and that gave me the idea to do this column. Now, I've got to warn you there are some serious mathematical calculations here, but don't let that stop you from continuing, because you do not need to understand the math in order to understand what I'm saying.

If you're an experienced Video Poker player, you already know that progressive 'jackpots' like a Royal Flush adds to the return that any machine offers. For example, a full-pay Jacks or Better game returns, to a skillful player, 99.54% of all the $$$ s/he runs through it - in the long run - and part of that return comes from the Royal. When the Royal is at 4000 coins, it contributes 1.98%, but as the Royal goes up in value, so does the overall return. So, if the Royal's at 5000 coins, say, the total return is 100.06% and the Royal's contribution is 2.80% or 0.82% more. You'll immediately notice that the total return has gone up only 0.52%, so some of the 0.82% gain from the Royal has been lost! That's because such a large increase in the Royal requires some playing strategy changes, so the return from other hands will decrease. A good example of this is in the hand of a pair of Jacks. When the Royal's at 4000, a 'high' pair contributes 21.46% to the overall return. But, when the Royal's at 5000 coins, a pair of Jacks (or better) returns 21.26% which obviously 0.20% less and that's two-thirds of the 'loss'. This happens because of the strategy changes; it's very proper to break a high pair in order to draw to some (not all) 3-card Royals which may also make up the hand. When you do that, you're throwing away a hand which pays at least 5 for 5 and it's not likely that you'll get the Royal, but it's the correct play even though you'll probably end up with a hand that pays nothing at all.

"Ah, ha" I hear you say, "what if I don't make that play and keep the pair instead?" Well, that won't work because it just increases the number of hands you'll need to play in order to hit the Royal so it will, even at the higher value, only contribute 1.98% to the overall return. That may be a bit confusing, so let me explain a bit. If one uses perfect playing strategy, a Royal will occur in a Jacks game every 40,400 hands. But, if adjustments to the playing strategy are made when the Royal's at 5000 coins, it will happen once every 35,725 hands. In other words, you get more $$$ and you get them quicker, but it's at a cost because you're throwing away hands like a pair of Jacks to do that. If you don't make the strategy changes, it will still take 40,400 hands for it to come in and, because the return on the game is well below 100% (not counting the Royal), you'll have a bigger loss to make up for when the Royal finally does arrive.

What all this means is that you're raising the variance of the game. Without getting overly scientific here, variance is described as the difference between the theoretical and reality. If you toss a coin 100 times, the theoretical result is 50 heads and 50 tails. But the reality may be that you'll get a result of 55 heads and 45 tails. Do another 100 flips and you may get 51 heads and 49 tails and so on; you get the idea. Those results are called 'dispersion' and they form the basics for variance. The variance of a particular game is of little use to the gambler, at least on its own. But, it's of considerable value as a basis of comparison such as deciding which Video Poker game to play. Another example: A full-pay Jacks game with a 4000-coin Royal has a variance of 19.51 per coin bet and a full-pay Double Bonus game with a 4000-coin Royal has a variance of 28.26 per coin bet. Obviously, the DB game has a considerably higher variance which basically means that it takes more $$$ to play the same number of hands at that game than a Jacks game. Double Bonus pays only 5 for 5 on two-pair and that's a large reason why it takes more $$$ to play than a Jacks game which pays 10 for 5 on the same hand. However, a full-pay DB game returns 100.17% for perfect play and the Jacks returns only 99.54%. But (and here we arrive at the crux of this column), how does variance compare when the Jacks game is at the same return? Of course, to get to that return, the progressive has to be higher and, since the vast majority have a progressive Royal, we'll use that as our example. To get to the same return as a full-pay Double Bonus game (100.17%), a 9/6 Jacks game needs a Royal at about 5200 coins. And the variance? Oh, it's now 34.44. Yep, you read it right; the variance has almost doubled and it's now even more than the Double Bonus game! I've got to tell you that I was surprised when I saw that. I knew the variance would go up, because more of the return is in a hand which occurs rarely, but I didn't know it would exceed that of the DB game.

So what's this mean to you? Maybe nothing if you play just Jacks games, but if you want to play at games with 100+% paybacks, then you might choose to play some where the return is boosted by a progressive. If that's the case, the variance can help you decide which to play. Here's an example. At one casino I frequent, there is (at least, was) 10/7 Double Bonus Poker available and it returns 100.17% for perfect play. There is also a 9/7 DB game with a progressive Royal. When the Royal is at 6000 coins, that game returns about the same; 100.14%. The variance on the 10/7 game is 28.26 and for the 9/7 it's 56.66, or about double. The primary reason for that is the contribution of the Royal. In the 10/7 game, the 4000-coin Royal adds 1.67% but in the 9/7 game, the 6000-coin Royal adds 3.46% to the total return. Are you getting it now? It's not only important that the total return is 100%, but it's where that 100% comes from. If a relatively large part of it is from a rare hand like the Royal, the variance skyrockets. (I won't even mention the tax implications of a $1000 jackpot vs. a $1500 jackpot.)

How would you like to play a 9/7 Double Bonus game with a 101.55% return and a variance of 28.11, which is less than that of the 10/7 game? Well, if we can convince some casino owner to offer a 9/7 DB game where two-pairs pays 6 for 5 instead of 5 for 5, that's what we'd have. That's not going to happen, of course, but it really does a good job of explaining "variance". The return is higher but the variance is lower because the increase in the return comes from a hand which occurs quite frequently.

This has gone on much longer than I intended, so I'll do another installment next time where I compare games with 100+% returns and their variances.

See you then.

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