JoeChess Chess Piece Mortality

I work for Milliman USA, an Actuarial firm headquartered in Seattle.  I am not an actuary but I work with them all the time.  (Many JoeChess players are, in fact, actuaries.)  With that motivation, and due to the completion of my boat, the not so great weather, and an abysmal social life I have completed a study of JoeChess Chess Piece Mortality.  I took move by move data from the JoeChess database as of about 4/30/2003 and analyzed the records in Excel.  At that time, there were some 308 completed games (non-forfeits and non-declines).

Assumptions:

• Pieces are "killed" and not "captured".
• The object of a JoeChess game is regime change.  Resigned games result in the immediate execution of the resigned king.  Surviving defeated pieces are considered "enemy combatants."  While they are denied all civil liberties, they are not killed.
• Both kings survive in the case of a draw.
• There are no other causes of chess piece mortality except the battlefield.
• For the purpose of calculating expected lifetimes, we assume that the universe ends at the end of the longest game.

Each piece death is counted on the turn of it's death.  I gathered piece type, piece color, and the rating of the owning player (rating as of 4/30/2003, not rating at time of play).

Chance of Dying By Age x

The easiest thing to compute is the overall chance of death of a piece- total deaths over starting population.  It's also pretty easy to do that turn by turn by taking the (cumulative) deaths at turn x divided by the starting population.  The following chart shows these results.  I was surprised to see that being a pawn isn't really so bad!

Rooks have about as good a survival chance as pawns, followed closely by the kings themselves.  Sucks to be a knight though!

But, since games are of different length, this view hides information- we can't really tell when the endgame starts for example.  Let's do some more analysis.

Chance of Death at age x

Mortality tables for insurance and annuities are developed by starting with a list of probabilities that give the odds for surviving from one age to the next.  These are the "q"s.  To develop these, I take the population at age x+1, subtract the population at age x then divide by the population at x and call that q(x) - the probability that a piece alive in turn x will not make it to turn x+1.  Note the difference from above - above at turn 36 we see that a pawn has about a 38% chance of being dead.  Below, what we see is that a pawn in a game has about a 1% chance to get to turn 37.

A real actuary would probably do some smoothing.  But even so, you can get a pretty good idea of how the games progress.  We can see prime pawn killing time peaks early, while rooks and kings don't start buying their farms until later.  But pawn death rates are low - how can we tie it all together?

Life Expectancy

What I was really interested in this study was life expectancy - how long can a typical JoeChess chess piece expect to live?  Are there any differences between black pieces and white pieces?  What about the wielding player?  Does a better player give his pieces longer life, or does he (or she) spend them recklessly in pursuit of victory?  We've got the data, let's take a look!

Not surprisingly, kings of players with rankings > 1200 are the longest lived.  (1200 was chosen as the breaking point since it is the default starting value of a JoeChess player.)  Pawns and rooks are a close second.  All you insurance guys take note - jack up the premiums on knights and bishops!

Conclusion

Well, the only thing that I can conclude is that I really need to get out of the house more often.  If anybody wants the raw data, you can download it here: ChessMortality.zip