Thrill Digger and expected value

I got my copy of Skyward Sword last week, and so far, I've been having a blast. Recently, though, I was running Link up a volcano, on his way to find Zelda, and I got sidetracked by a mini-game called Thrill Digger.

Fortunately, I could take my time, and play around with it without worrying about Zelda too much.

So Thrill Digger is a gambling game. You pay a fee to play, then get to choose points on a grid - some grid points contain money, some contain bombs. You get to keep choosing points until you find a bomb, and which point the game ends. You get to keep all the money you find.

Money in Hyrule comes in a few denominations:

• Green Rupees are worth 1
• Blue Rupees are worth 5
• Red Rupees are worth 20
• Silver Rupees are worth 100
• Gold Rupees are worth 300
• Black Rupees (aka Rupoors) are worth -10

There are three levels of play:

The Beginner difficulty costs 30 Rupees to play, and consists of twenty spaces in a 5x4 grid. Of these spots, four are bombs. The grid is guaranteed to hold a number of both Green and Blue Rupees, with a small chance of a Red Rupee.

The Intermediate difficulty costs 50 Rupees to play, and consists of thirty spots in a 6x5 grid. Of these spots, four are Rupoors and four are bombs. The grid contains mostly Blue and Red Rupees, while Green and Silver Rupees are fairly rare.

The Expert difficulty costs 70 Rupees to play, and consists of forty spots in an 8x5 grid. Of these spots, eight are Rupoors and eight are bombs. Most spots contain Red Rupees, and occasional sightings of Blue, Silver, and Gold Rupees have been observed.

Now here's where the game gets interesting.

The type of Rupee in a dig spot identifies how many Bombs and Rupoors are in the eight spots around it, as follows:

• Green Rupee: 0 spots
• Blue Rupee: 1-2 spots
• Red Rupee: 3-4 spots
• Silver Rupee: 5-6 spots
• Gold Rupee: 7-8 spots

This makes it quite hard to determine exactly how many spots are covered. Link can uncover all spots around Green Rupees without harm, while it's probably a very good idea to avoid all spots around a Gold Rupee.

Rupoors identify as a bomb for the purposes of which type of Rupees surround it, and will subtract 10 Rupees from Link's current total, but do not end the game

This makes the game somewhat like an imprecise version of Minesweeper (with a bit of Memory for flavor, since what grid spots used to contain before you dug there is not displayed).

In Minesweeper, however, the goal is to discover the mine locations. There's no cost to starting a new game, and no extrinsic value to revealing that a square does not contain a bomb.

By placing an upfront cost on playing, and shifting the goal from "discovering the mine locations" to "find as much money as possible", this changes the nature of the game. We want to get close to bombs and rupoors (so as to find high-denomination currency), but avoid them.

With this explicit cost/reward structure, we could calculate the expected value of a game of Thrill Digger. Even more, we could construct a Thrill Digger assistant, which, given the current game state, could advise us on the most advantageous location to dig next.

Sound like fun? I know it does to me :) So look for something in this space about my Thrill Digger assistant in the future.