Variance in Double Joker Poker Progressive

Using Bob Dancer's WinPoker software for analysis, here are the expected return (with perfect play)
and variance for 3 variations of Double Joker Poker Progressive:

Royal Flush pays 4000. Expected return is 98.1005%. Variance is 21.81212

Royal Flush pays 8000. Expected return is 99.9132%. Variance is 66.43613

Royal Flush pays 8192. Expected return is 100.0015%. Variance is 69.29956

Since only the RF payoff is different, why does the variance increase so much?

Quote: bluemartin

Using Bob Dancer's WinPoker software for analysis, here are the expected return (with perfect play)
and variance for 3 variations of Double Joker Poker Progressive:

Royal Flush pays 4000. Expected return is 98.1005%. Variance is 21.81212

Royal Flush pays 8000. Expected return is 99.9132%. Variance is 66.43613

Royal Flush pays 8192. Expected return is 100.0015%. Variance is 69.29956

Since only the RF payoff is different, why does the variance increase so much?

Because whether or not you finish a session ahead depends heavily on whether you hit the royal, and when you do, you finish MASSIVELY ahead. Thus, you either lose a fair amount (most of the time), or win a huge amount (some of the time). The royal stretches the bell curve waaaaaay out to the right.

I agree with that answer but don't understand how it explains the hugh difference in variance between the RF=4000 and RF=8000 versions of Double Joker Poker Progressive cited above. I thought variance was a measure of how "streaky" a video poker game was likely to be. A low variance indicates that you are likely to get a lot of small wins that allow you to keep playing a longer time on a given bankroll. A high variance indicates that you are likely to use up your bankroll sooner unless you are lucky enough to hit some of the higher payoff hands. So someone with only a small bankroll could typically expect to play longer on a low variance game than on a high variance game. Is that wrong? Where can I find a detailed definition/explanation of variance?

Variance is the square of the standard deviation. However, I doubt that helps you much.

Visualize a bell curve. The highest point is the mean result. The curve does not have to be symmetrical; in fact, for video poker, it is usually longer horizontally and shorter vertically than the left side. This is because it is very unlikely to have a result of -800 units (impossible if you play less than 160 hands), but it is quite possible to have a result of +800 units (i.e., a royal). This is the standard type of distribution for video poker games.

A more volatile game, such as Double Bonus, will have a wider and less tall bell curve, because results "out on the ends of the curve" are more likely. Conversely, in a game like Jacks or Better, the curve will be tall and kind of pudgy. Joker Poker falls somewhere in between these extremes.

Now, imagine that the royal flush is worth 1600, not 800 bets, but everything else stays the same. The point representing the "got a royal flush" result moves twice as far out to the right (positive result), and the curve has to stretch to follow it. Thus, variance is increased.

This is obviously an improvement. Variance is not necessarily a bad thing. The difference, in this case, lies in the increased magnitude of the royal flush win; everything else remains the same, especially the left-hand portion of the bell curve. To further illustrate, suppose that the paytable was further altered--by, say, reducing the payout on the full house by one unit--to "compensate" for the doubled royal payout, so that there was no increase in player EV. That would create a situation where variance was increased WITHOUT an increase in EV, and would be "neutral" in terms of player effect--both your wins and your losses would be bigger. The increase in variance in the game we've been discussing, however, is because only your WINS are bigger.

There is a minor modification to the above, in that you should be more aggressive in pursuing the royal, which means you will be giving up some small wins to go for the biggie, which will, in turn, increase your variance. I don't know if the variance figures you quote take that into account.