Can I ever stop doing math?

I’m still trying to shake the worst of a cold, so the XBox 360 is getting a bit of a workout. I usually only play video games when I’m sick and/or tired, just as some relaxation and diversion. Games which are too involving, requiring long quests aren’t really in the mix for the most part, since I don’t really feel like dedicating that much time to them.

Nevertheless, Carmen picked me up a copy of Mass Effect, what is essentially a space opera based role-playing game, where you play a hero trying recover an alien artifact, yada yada… it’s reasonably well done, but the game play has a bit too much running around on side quests for my taste. And, like virtually every RPG type game, the majority of your time seems to be spent trying to find/buy upgrades to your skills and equipment. Honestly, this kind of game usually doesn’t appeal to me very much: it’s like working a job. But this game is, I must admit, better and more imaginative of its genre, so I am about four or five hours into it.

But back to the math:

Inside the game there is a casino called “Flux” which houses a bunch of machines upon which you can play a casino game called Quasar. It’s sort of like a stripped down version of Blackjack. The idea is that you try to get a score as close to 20 as you can (without going over). In each step, you can either a) hold with what you got b) choose the X strategy, which adds a number from 4-7 inclusive to your count, or b) choose the Y strategy, which adds a number from 1-8 to your total. The game costs 200 quatloos (or whatever) to play, and payouts vary according to your total.

Total Payout
15 50
16 100
17 200
18 250
19 300
20 400

(The reality of the game is that you actually can’t hold on any total less that 15, but since that strategy would always guarantee the maximum possible loss in all situations, it hardly matters in determining the optimal solution.

Anyway, I wrote a little Python script to compute the optimal strategy, which can be summarized
as follows:

If your total is 17 or greater, then you hold and collect your winnings.
If your total is 16, choose strategy Y.
If your total is 15, choose strategy X.
if your total is 1, 2, 6, 7, 8, 13 or 14, pick strategy X.
Otherwise, pick strategy Y.

It isn’t clear to me how the game picks your initial count. In the ten or 15 minutes that I’ve played the game, it seems to me that the initial count is perhaps uniformly distributed between 1 and 5 (inclusive). This amounts to an average net profit to the player of about 40 quatloos per round. Hence, it takes about 25 rounds to make 1000 quatloos.

The best numbers to get are 13, 7, 12, 6, and 1. The worst? 16, 15, 9, 10, 11, although only 16 and 15 have a negative expectation.

I’m doped up with cough medicine, have a sinus headache, and yet here I am, writing programs and doing math instead of playing a video game. I must be crazy.

Addendum: There are many sites that also derived the same strategy, like this one. Google for more if you’d like.