Help me craft a winning Pokewalker strategy

The Game Room
1

So, Bricker Jr. has the new Pokemon HeartGold game. It comes with a pedometer that can be used to augment the game play, and itself has a couple of minigames, one of which occasions this thread.

The “Dowsing” game has six little bushes, all in a row, from one to six:

X–X--X–X--X–X

You have two tries to discover which bush has a hidden item under it. Your first pick has no clues to guide it. If you fail to select the right bush, the game then gives you one of two clues: “It’s near,” or “It’s far away.”

“Near” means immediately adjacent to the bush you tried. “Far away” means “not immediately adjacent.”

So what strategy should a player use to maximize his chances of selecting the correct hiding place?

2

L has this game, although she is not going to ask her Old Stepdad for help.

The way I see it, you have two methods of playing this game. You can look at #3 then #5, or you can look at #2 then #5. The theory is that on the first two choices, you want to maximize your chances of getting a “near” or a hit. By choosing two interior bushes, you have a better chance of getting a hit.

Counterintuitively, the #3 then #5 strategy is better. Here’s the methodology behind that. If the item is under #1, then it will take three tries to find it under 3-5 (you pick #3, then #5; since the item will be “far away” on both choices, #1 is the only place it can be), and 2.5 tries under 2-5 (you pick #2, it says “near”, so you pick #1 or #3, so it’s going to be either two or three tries). Similar analysis results in this table:

 3-5    2-5

1 3 2.5
2 2.5 1
3 1 2.5
4 2.5 3.5
5 2 2
6 3 3.5

Add them all up, and the “choose 3, then 5” strategy gives you an average of 14/6 choices to get the hidden item, or 2.33 choices to get the item. “Choose 2, then 5” strategy gives you 15/6 choices to the item, or 2.5. So, by a small margin, it’s better to pick 3, then 5.

3

So, you get one try, then you get a clue, then you get another try, and if you don’t get it the game is over, right?

In that case, then all strategies are identical.

You basically have two choices: one of the end pieces, or a piece somewhere in the middle.

Odds for the end piece:

Obviously, if the thingy is under the one that you pick, you win. Yay!

If you get “near”, you know with 100% certainty where the other piece is, and thus win.

If you get “far”, you have a 1 in 4 chance of guessing right.

Out of the 6 possible placements, there are 2 that give 100% returns and 4 that give 25% returns; (2 x 1 + 4 x .25)/6 = 50% chance of winning.

Odds for the middle piece:

Again, 100% if the thingy is under your first choice.

If “near”, you have a 1 in 2 chance of finding it.

If “far”, you have a 1 in 3 chance of finding it.

(1 x 1 + 2 x .5 + 3 x .333…)/6 = 50% chance of winning.

So it’s purely a game of chance.

(If there were more than 2 tries, there might be strategies possible - not sure about that.)

4

I forgot to ask…are there only 2 choices available? In that case, the best strategy is to simply choose one of the four interior bushes. Choose 2, 3, 4, or 5: 1 chance in 6 of getting it right on Choice #1. If you get the response “near”, you have a 1 in 2 chance of getting it right by choosing one of the adjacent bushes. If you get the response “far away”, you have a one in 3 chance of getting it right by choosing one of the three other bushes.

And that’s as good a strategy as you can hope for.