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How to Generate OTB Random Positions. How to generate random positions?
Thomas McElmurry wrote on 2009-08-06 UTCGood ★★★★
I expect this will be a very useful reference for newcomers to random variants, and probably for some not-so-newcomers as well.

I have a couple of quibbles, though, about probability. In my view, a good randomizing algorithm must ensure that all positions occur with equal probability (unless there's a good reason to do otherwise).

1st quibble: When same-color bishops are allowed, it's best to treat the bishops the same as any other piece, and simply not think about square colors when placing the bishops. If you use procedure 3.2, you'll skew the probabilities. For example, let's check the numbers for Modern Random Chess. [I'll use the notation nCr to denote the binomial coefficient 'n choose r'.] Suppose we place the bishops first, before any other pieces. We have 9 squares on which to place 2 bishops, so there are 9C2 = 36 possible placements for the pair. Let's see how these stack up in terms of color configuration, noting that the first rank has 5 dark and 4 light squares. There are 5C2 = 10 placements with both bishops on dark squares, 4C2 = 6 placements with both on light squares, and (5C1) (4C1) = 20 placements with one bishop on each color. But procedure 3.2 generates dark-dark placements with probability 1/4, light-light placements with probability 1/4, and light-dark placements with probability 1/2. This means that light-light placements will occur 50% more often than they should, and the others will occur less often than they should.

2nd quibble: With the constraint that the king must be placed between the two rooks, it's dangerous to place one type of piece before the other as in procedure 4.2–4.3. In Fischer Random Chess, for example, there are 108 positions with the white king on b1, 168 with the king on c1, 204 on d1, 204 on e1, 168 on f1, and 108 on g1. But if the king is placed first, it goes to any of these six squares with equal probability. (Note also that the Game Courier preset uses this method; thus FRC as implemented in Game Courier is biased toward positions with the kings on the flanks.) It's safer to leave the kings and rooks until the end as in 4.1.

Jose Carrillo wrote on 2009-08-06 UTC
Thanks for your comment Thomas. As I said this was by no means an all inclusive list of processes for randomizing positions. It was meant to have a stake in the ground on generating random positions for OTB games, and a place to comment on other methods, probabilities, etc. about random positions. I agree with your comment on the same color Bishops. The reason of some of my options is to keep the process simple with handy equipment. Of course if everyone (like myself) carried a 10-sided dice around then matters would be a lot easier for randomizing. But the fact is that a 6-sided dice and a couple coins are easier to find, so I setup simple procedure accordingly. Remember these procedures are intended for OTB games. How many random OTB games do you expect to play in one sitting? Not enough to matter.