### The 15-wheeler truck in 9/7 Triple Double Bonus Poker

9/7 Triple Double Bonus is a pretty volatile game. It looks like its strategy is also rather wild!

It’s so wild, I can’t tell you the *best* basic strategy for 9/7 Triple Double Bonus. Yet. That’s because my software is still calculating it!

You may wonder why it’s taking so long. It’s because there are fifteen different options, some of which better than another, that don’t easily let themselves get sorted in a simple order. For example, ** 345** is on average better to hold than 55, 55 is better to hold than

**,**

*789***is on average better to hold than 77, and 77 is better to hold than**

*789***. In order to arrive at a basic strategy, I need to put these fifteen hands into some order. This order can’t be perfect, because there are several such loops among these fifteen options. But there is a best order, the order for which the strategy’s return would be maximized.**

*345*Unfortunately, there is no known fast algorithm for figuring out the best order among these fifteen hands (it’s actually an NP-hard problem, meaning if one finds a fast algorithm for the problem, they would also solve lots of open problems in computers science, something the best computer scientists have tried for decades and have yet to succeed at). So we may as well try all the different orders, and see which one has the highest return or lowest strategy error. That’s what my software is trying right now. There are 15! = 15 × 14 × 13 × ... × 3 × 2 × 1 = 1,307,674,368,000 different ways to order these 15 hands. That’s more than a trillion different ways (assuming you use the short scale).

The Wizard of Odds Video Poker Strategy Maker puts these hands in some order. I’m almost certain it’s not the best order, because it’s calculated so quickly. (I have noted before that it doesn’t calculate the best basic strategy for some games.) For the record, this is the order it puts the hands in:

* 789* > 88 >

**,**

*456***> 77 >**

*9TQ***,**

*345***,**

*89J***> TT >**

*8TJ***> 66 >**

*678***> 99 >**

*89T***> 55**

*567*So, I first set up my laptop to try all the 15! combinations, but it was a little slow. It looked like it will take my laptop about four days to find the best order. If not interrupted. But it gets interrupted too many times when it goes into sleep mode, and I’d rather not leave it up all night to discover it’s warmed up too much and melted something or caused a fire!

So I did what any sane computer scientist would do. I found a server in the cloud to run the calculations instead of trying them on my slow laptop. I uploaded my software to Google Compute Engine, and it’s now running there. The machines there are optimized for long calculations. And the servers are properly air conditioned too!

I’ll report back when I find the best basic strategy for 9/7 Triple Bonus. In the meanwhile, check out the figure at the top of this post, which has an arrow pointing from the better option to the worse option for each pair of options that can appear in a hand together. It looks pretty messy, despite my best efforts to provide the clearest version that I could. That’s because it’s messy by nature. The games with odd returns on flushes (5, 7, etc) seem to have such complex relations. I can’t really tell you why...

*Update: My software finished its work. I wrote about its results, as well as the best strategy for the game, here.*

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