So we have this new ladder feature, but all the calculations are undone!

Ok, it is obvious, that a player sinks down the ladder, when not challenging (e.g. on vacation ). But what is the average sink speed?

The climbing speed on the other hand depends on how many challenging games a player wins and how many defending games he looses, so if a player moves faster in the challenging games than the others he will be climbing up, even if not better than the others.

Let's make the usual simplifying assumptions.

( Let p be a zero-dimensional chess player in a one-dimensional ladder-world ;-)

Lets take a 1-day-ladder of n=1000 players, all players of equal elo r=1500,

All move 2 moves per day and game, a game has 30 moves average, there are no draws, its 50:50 who wins.

1. What is the average sink speed for a player who is on vacation?

2. What is the average rising speed for a player p, who plays 4 moves per day and game?

3. How fast must a r=1300 player in this ladder play, to continuously improve his rank?