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ajile
07-16-2010, 10:41 AM
Hi all,

Many of you I assume are familiar with Bejeweled, a puzzle game in which the player swaps neighboring, colored gems in an 8 x 8 grid to create rows and columns of ≥ 3 matching colors. My question pertains to what happens after a match is made.

Let's assume a horizontal match of 3 gems is made on the 5th row down. This causes these 3 gems to disappear, and for the gems in the 4 rows above them to "fall" into the empty space they leave behind. What I am trying to figure out is the probability that these falling gems (and the randomly generated new gems that appear on the top row) create a new match of 3 anywhere on the board.

Here is what we also need to know:
There are 7 gem colors.
There are 6 possible ways for a single, non-border gem to match with two of its neighbors.

Therefore the probability for three gems to match at random should be (1/7)^2, because the color of the first gem doesn't matter. Only the next 2 need to match each other and the first.

The formula I am trying to design would give the probability for a new 3-gem match resulting from a horizontal 3-gem match we make on the 5th row down.

So what I came up with was this: p = 3(((1/7)^2)*(6(r-1))) where r = the row on which the original horizontal match is made, and 6 is the number of ways a new, non-border gem can match with its neighbors.

Obviously, this is very wrong, and results in a value > 1 for our designated 5th row match. But I don't know how to fix it, or if there is a better direction entirely from which to attack this problem.

Thank you very much for your help on this!

Andrew

BGM
07-16-2010, 11:51 AM
So you need to clarify your problem a little bit.

1. Do you given the information/configuration/location of the original board of gems?
This information is very important as the color of the neighboring gems will determine
the probability of success.

2. "new 3-gem match resulting from a match": what does it mean?
Does it refer to ANY new match that does not exist before, but created due to the
downward movement/new gems? Or it only refer to the new gems?

ajile
07-16-2010, 12:08 PM
To clarify:

1. This is more meant to be a general formula, not for a specific scenario or board of gems, but applicable to any set of gems.

2. By "new 3-gem match resulting from a match" I mean yes, ANY match that did not previously exist. (And no previous matches could exist as they would have already matched and disappeared).

Please let me know if there is any further information I should be providing here. Thanks very much!