# Non-linearity in Armageddon bidding: Ostensibly, you give up more time in higher time control

Note: In the ff I assume everyone bids for black, not white.

# In blitz (below 10min) :

I see often there's a 5min vs 4min predetermined time. No idea if this is fair, but let's pretend arguendo players would really bid around 3:45-4:15 eg in the 2019 WFRCC and in the 2022 St Louis Chess 9LX in the 2022 women's US Chess Championship, Jennifer Yu vs Irina Krush.

• The ratio of black's time to white's time is 80% = 4min / 5min.

# In fast rapid (10min-32.5min) :

In the 2022 WFRCC and in the 2023 champions chess tour airthings masters, I notice they bid 9.3min for chess and 12.14min for chess960.

• In chess960, the ratio is still about 80%. It's 81% = 12.14/15.

• In chess, the ratio drops to 62% = 9.3/15.

# In slow rapid (32.5min-strictly below 60min)

(Actually I know of only 1 case.)

2013 USCC Alejandro Ramirez vs Gata Kamsky - The bid is 19:45 vs 45min. Since there's a 5 second increment, this converts to 24:45 vs 50min.

• The ratio has now dropped to below 50%, i.e. below half.

Question: Ostensibly, you are willing to give up more time in higher time controls. I guess it makes sense intuitively, esp in the reverse way: You are more hesitant to give up time in lower time controls. But I'm not sure how to explain this precisely. Why are players willing to give up more time in higher time control instead of just that the ratio is maintained throughout any time control?

Or well maybe it doesn't have to do with armageddon specifically. Maybe in general a game where players have remaining time 3min vs 6min is really different from a game where the same players have remaining time 30min vs 60min?

I believe there are two main reasons for this.

1. The draw rate increases as the time control increases.

From here the draw rate in chess for elite chess is roughly ~36% for classical, ~30% for rapid and ~18% for blitz. This gives a larger advantage to black, and therefore a bigger incentive to give up time in order to gain this advantage.

1. The performance drop-off for losing time is less at longer time controls.

Ken Regan shared a model of how much performance of elite players degrade at different time controls on the Perpetual Chess Podcast. His model there can be viewed here

He uses the orange line (formula of 338.845\ -\ \frac{1442}{x^{0.283638564}}). This means in order to give up 100 Elo (for example) in classical chess you could give up ~100 minutes out of 165 minutes (60% of your time). In rapid chess, it would be more like: ~14 minutes out of 30 minutes. (45% of your time). In Blitz chess, you would give up roughly 87s out of 5 minutes (~30% of your time)

You would need to give up more Elo to compensate for the increased draws of longer chess

To make these estimates concrete:

• For classical chess with a draw rate of 36%, you would want to give up ~131 Elo. This equates to bidding 52 minutes for a 165 minute game
• For rapid chess with a draw rate of 30%, you would want to give up ~107 Elo. This equates to bidding 13:45 for a 25 minut game.
• For blitz chess with a draw rate of 18% you would want to give up 63 Elo, this equates to bidding 3:57 in a 5 minute game.

There is probably an additional third reason, which is that elite players have a "drawing repertoire" with black where they play more solidly for a draw. This repertoire probably has more force in longer time controls where they can find strong moves if white attempts to complicate. I don't think I'm a good enough player to comment on whether how much this is the case

Maybe in general a game where players have remaining time 3min vs 6min is really different from a game where the same players have remaining time 30min vs 60min?

Yes, it's very different. In 30 vs 60 minutes the performance drop off (in Elo) is ~100 Elo. In 3 vs 6 minutes the performance drop off is more like ~190 Elo.