How Much Does Complexity Cost

The following question was posed to me for inclusion in one of Richard’s and my mailbag shows on our Gambling with an Edge podcast. While I did give an answer to it on the air, I believe a fuller answer is appropriate and so I’m going to talk about it here as well.

“This version of Double Bonus Poker is called “Full Pay Double Bonus Poker” or “10/7/5 Double Bonus Poker.”

If Jacks or Better and Double Bonus Poker had similar strategies, it would be a no-brainer to select Double Bonus Poker as the preferred game.

Unfortunately, the strategy for Double Bonus Poker is more complex than the strategy for Jacks or Better making it more likely that mistakes will be made – mistakes which will cost you money.”

The above quote was written by a gaming columnist. I had thought that a 9/6 Jacks or Better strategy for 10/7 Double Bonus gave you a better return than it does for Jacks or Better. What do you think, Bob?

Everything alluded to in the quotation and the question is correct. 10/7 DB does return more than 9/6 JoB; 10/7 DB is much more complicated than 9/6 JoB; making mistakes is costly; and using 9/6 JoB strategy on 10/7 DB returns more than using the same strategy on 9/6 JoB! It sounds like a riddle of sorts, but it’s all true.

10/7 DB returns 100.17% when played perfectly. 9/6 JoB returns 99.54%. Playing 10/7 DB using 9/6 JoB strategy returns 99.63%, which is more than 99.54%. Even though you’re using a non-optimal strategy for 10/7 DB, you’ll end up with enough quads, full houses, flushes, and straights (all of which pay more in 10/7 DB than they do in 9/6 JoB) so your net return is higher than if you played 9/6 JoB with the same strategy.

So, the obvious conclusion is that if you know 9/6 JoB strategy and 10/7 DB is available, it’s better for you to use that strategy on 10/7 DB. There are at least a few problems with this conclusion.

First of all, there’s variance. 10/7 DB has a variance of 28.3. 9/6 JoB has a variance of 19.5. An appreciation for higher variance is not universal.

The reason for the higher variance is centered around the two pair hand, which occur every 7.74 hands in JoB and every 8.02 hands in DB. If you play several hundred hands today, you’re going to hit about the right number of two pair hands. 

The hands that pay more in DB, particularly the quads, occur much less frequently. The highest pay quad, aces, occur every 5,030 hands if you’re playing correct DB strategy, and every 5,111 hands if you’re playing correct JoB strategy. Playing several hundred hands today you may or may not hit that hand. 

So using the 9/6 JoB strategy on 10/7 DB does return a little more, but it’s a bumpier ride. You’ll have more losing sessions, but your winning sessions, when you get them, will be bigger. Is that a good tradeoff for you? (It would be for me — but I’m not the sort of player whose going to be using 9/6 JoB strategy on 10/7 DB. I’ve learned the correct strategy, and using that pays a lot more than using the 9/6 strategy.)

In addition to your taste for variance, at some casinos the slot club treats 10/7 DB differently than it does 9/6 JoB. Back in the mid-1990s when I first wrote about playing 10/7 DB with 9/6 JoB strategy, I didn’t take the slot club into effect because at that time, in every casino so far as I knew, all video poker machines had the same slot club return. No more. Today you may well earn half points, or even quarter points, playing a 10/7 DB machine compared to what you’ll earn playing a 9/6 JoB machine.

Whether or not the difference in slot club points is enough to determine which is the better play depends on the casino. Every casino has its own formulas. And they change over time.

This is not a difficult math problem, but it’s more difficult than many players wish to deal with. Unfortunately, I don’t have a one-size-fits-all conclusion. As with many things in video poker, it depends.