Answers.Body: <p>I believe there are two main reasons for this.</p>
  <ol>
  <li>The draw rate increases as the time control increases.</li>
  </ol>
  <p>From <a href="https://www.chess.com/blog/ThomasJEvans/drawing-rates-in-chess-pt1---time-matters" rel="nofollow noreferrer">here</a> 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.</p>
  <ol start="2">
  <li>The performance drop-off for losing time is less at longer time controls.</li>
  </ol>
  <p>Ken Regan shared a model of how much performance of elite players degrade at different time controls on the <a href="https://www.youtube.com/watch?v=UsEIBzm5msU&amp;t=617s" rel="nofollow noreferrer">Perpetual Chess Podcast</a>. His model there can be viewed <a href="https://www.desmos.com/calculator/do7pbyh5ay" rel="nofollow noreferrer">here</a></p>
  <p>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)</p>
  <p>You would need to give up more Elo to compensate for the increased draws of longer chess</p>
  <p>To make these estimates concrete:</p>
  <ul>
  <li>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</li>
  <li>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.</li>
  <li>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.</li>
  </ul>
  <p>There is probably an additional third reason, which is that elite players have a &quot;drawing repertoire&quot; 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</p>
  <hr />
  <blockquote>
  <p>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?</p>
  </blockquote>
  <p>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.</p>
  
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Body: <p>Note: In the ff I assume everyone bids for <a href="https://chess.stackexchange.com/questions/41552/why-would-i-bid-for-white-in-armageddon-in-regular-chess">black, not white</a>.</p>
  <h1>In blitz (below 10min) :</h1>
  <p>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 <a href="https://chess.stackexchange.com/questions/41534/what-were-all-the-chess960-armageddon-games-played-in-st-louis-chess-9lx-and-the">the 2019 WFRCC and in the 2022 St Louis Chess 9LX</a> in the <a href="https://www.youtube.com/watch?v=zGO_rm4UStE&amp;t=3773s" rel="nofollow noreferrer">2022 women's US Chess Championship</a>, Jennifer Yu vs Irina Krush.</p>
  <ul>
  <li><strong>The ratio of black's time to white's time is 80%</strong> = 4min / 5min.</li>
  </ul>
  <h1>In <a href="https://chess.stackexchange.com/questions/41478/how-does-fide-define-slow-rapid-fast-rapid">fast rapid</a> (10min-32.5min) :</h1>
  <p>In the 2022 WFRCC and in the 2023 champions chess tour airthings masters, I notice <a href="https://chess.stackexchange.com/questions/41586/armageddon-how-much-more-desirable-is-black-in-chess-than-chess960-based-on-air">they bid 9.3min for chess and 12.14min for chess960</a>.</p>
  <ul>
  <li><p>In chess960, the ratio is still about 80%. It's 81% = 12.14/15.</p>
  </li>
  <li><p><strong>In chess, the ratio drops to 62%</strong> = 9.3/15.</p>
  </li>
  </ul>
  <h1>In slow rapid (32.5min-<a href="https://chess.stackexchange.com/questions/41499/why-was-the-2019-wfrcc-called-slow-rapid-when-its-actually-classical-4515-6">strictly below</a> 60min)</h1>
  <p>(Actually I know of only 1 case.)</p>
  <p><a href="https://www.youtube.com/watch?v=m3Ova9ucsHk" rel="nofollow noreferrer">2013 USCC Alejandro Ramirez vs Gata Kamsky</a> - The bid is 19:45 vs 45min. Since there's a 5 second <a href="https://chess.stackexchange.com/questions/41576/is-armageddon-always-without-increment-should-it-be">increment</a>, this <a href="https://chess.stackexchange.com/questions/41479/time-control-conversion-when-it-comes-to-bonus-time-after-eg-40-moves">converts</a> to 24:45 vs 50min.</p>
  <ul>
  <li><strong>The ratio has now dropped to below 50%, i.e. below half.</strong></li>
  </ul>
  <p><strong>Question</strong>: 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. <strong>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?</strong></p>
  <p>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?</p>
  
Tags: <statistics><time-control><mathematics><armageddon>
Title: Non-linearity in Armageddon bidding: Ostensibly, you give up more time in higher time control
ThreadText: # Non-linearity in Armageddon bidding: Ostensibly, you give up more time in higher time control
  
  (Asked by: username_0 on 2023-02-11)
  
  Note: In the ff I assume everyone bids for [black, not white](https://chess.stackexchange.com/questions/41552/why-would-i-bid-for-white-in-armageddon-in-regular-chess).
  
  # 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](https://chess.stackexchange.com/questions/41534/what-were-all-the-chess960-armageddon-games-played-in-st-louis-chess-9lx-and-the) in the [2022 women's US Chess Championship](https://www.youtube.com/watch?v=zGO_rm4UStE&t=3773s), Jennifer Yu vs Irina Krush.
  
  * **The ratio of black's time to white's time is 80%** = 4min / 5min.
  
  # In [fast rapid](https://chess.stackexchange.com/questions/41478/how-does-fide-define-slow-rapid-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](https://chess.stackexchange.com/questions/41586/armageddon-how-much-more-desirable-is-black-in-chess-than-chess960-based-on-air).
  
  * 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](https://chess.stackexchange.com/questions/41499/why-was-the-2019-wfrcc-called-slow-rapid-when-its-actually-classical-4515-6) 60min)
  
  (Actually I know of only 1 case.)
  
  [2013 USCC Alejandro Ramirez vs Gata Kamsky](https://www.youtube.com/watch?v=m3Ova9ucsHk) - The bid is 19:45 vs 45min. Since there's a 5 second [increment](https://chess.stackexchange.com/questions/41576/is-armageddon-always-without-increment-should-it-be), this [converts](https://chess.stackexchange.com/questions/41479/time-control-conversion-when-it-comes-to-bonus-time-after-eg-40-moves) 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?
  
  **Tags:** statistics, time-control, mathematics, armageddon
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2023-02-11. Score: 3 | Accepted answer
  
  I believe there are two main reasons for this.
  
  1. The draw rate increases as the time control increases.
  
  From [here](https://www.chess.com/blog/ThomasJEvans/drawing-rates-in-chess-pt1---time-matters) 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.
  
  2. 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](https://www.youtube.com/watch?v=UsEIBzm5msU&t=617s). His model there can be viewed [here](https://www.desmos.com/calculator/do7pbyh5ay)
  
  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.
  
  
  ---
  
  