How many komi is reasonable for the colour white, when you play on a 13 x 13 bord.?
The default komi is 5.5 because OGS follows the old Japanese recommendation. This value is reasonable based on the expected win/loss ratio of each side across most levels of play.
It looks like the old Japanese recommendation was basically that komi should remain the same, regardless of the size of the board. Following this recommendation, standard komi should be 6.5 across all boards, since standard 19x19 komi has changed from 5.5 to 6.5 under Japanese rules.
I really don’t know if that’s actually considered fair for 13x13 or not, I’ve simply not played much 13x13 – but I was always under the impression that komi for 9x9 play should remain at the same as for 19x19 for each ruleset.
Komi is compensation for black going first so in 19 by 19 board it’s 6.5, in to my opinion on smaller board first move should compensate with same value. Because first move value is at lease the same on smaller than on bigger board (or even bigger).
I also think that Komi should rather be higher … see discussion on the page @mark5000 linked to, esp. http://senseis.xmp.net/?HandicapForSmallerBoardSizes#toc5