BB: Aye. Hypergammon has a higher luck component than Backgammon. How do you quantify the luck in Battleboats? There's a small but discernable degree of luck in Dark Chess. Different formulas for each would be appropriate.

But just two - the Chess one for games of pure skill and the Backgammon one for games with chance in them - that would be a good compromise and easy to implement.


As an example:
A top player here (BKR 2540) plays a single match against someone of 2400 points. It will be a gain of +5 for a win and a drop, -11, for a loss. That means that the higher player must win 2 out of every 3 games. Such a small rating difference does not reflect such a degree of difference in skill. In the example given the two players are well matched. The lower rated one has won 9 matches so far and the higher player has won 8.

Using the well established Backgammon formula (top player's rating at 2100 and lower player at 2000) the points would be 1.88 for a win and -2.12 for a loss. That ratio better reflects the skill differential: 52.9% winning chance for the higher player, 47.1% for the lower (and the points in inverse proportion).

Also noteworthy is that the match itself, being a single pointer, is only worth 4 points in total rather than being worth 16 as in the BKR example.

I hope it is clear from the example above that the Chess formula is unfair - and this is of a top 5 player playing a top 20 opponent!

When it comes to a high rated player against a much lower player, say a player 300 points lower (which is still top 70 and a strong opponent), the formula makes it highly punitive. A drop of 14 points for a loss and only 2 gained by a win! That means the higher player must win 7/8 matches just to stay even. There is no way that a 300 rating point difference can be justified by that.

Even against an average player, and Reza gives himself as an example, the top player will lose a substantial percentage of games because of the Dice Gods. (The Backgammon formula predicts 30%). The Chess formula's ratio of -14:+2 and worse will make higher ratings plummet as a result of normal losses in tournament matches - and that's a good reason to feel wary about joining them.