Answers.Body: <p>I have to admit I found the Wikipedia article on fair cake-cutting pretentious in the extreme. Why Lebesque Measure needs to be dragged into cutting a cake is beyond me despite being a mathematician who knows what Lebesgue measure is.</p>
  <p>Going back several decades to my university flat-sharing days, the standard solution to the pizza cutting problem (when we ordered a pizza take out to share between us) was that one person cut and the other person chose. When there were more than two of us the person cutting chose last. That way the person cutting had the motive to cut as evenly as possible.</p>
  <p>That's not quite analogous to the Armageddon colour choice problem. In cutting a cake or pizza the person choosing has full information. They can see exactly what the situation is. The chess colour choice is different. The second player doesn't know what the first player has bid. However both players can evaluate what the value is of playing black in relation to the other player and bid accordingly.</p>
  <p>What the two ways of choosing <em>do</em> have in common is that they both allow the players / eaters to judge their own best interests and choose, either a slice (to make with a knife or to eat) or a time, accordingly. That way none of the players / eaters can claim that the system was unfair to them, which players assigned black or white by chance might think.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-02-06T05:57:25.093Z
Answers.Text: Brian Towers♦ Is it wrong to think this way? 'smaller piece = lower time + black' but 'the strawberry on the smaller piece = draw odds' ? So you can have a smaller piece that is more delicious or a bigger piece that is less delicious. Quote on Wikipedia: 'If a cake with a selection of toppings is simply cut into equal slices, different people will receive different amounts of its toppings, and some may not regard this as a fair division of the cake.'
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-02-06T06:55:48.680Z
Answers.Text: "In cutting a cake or pizza the person choosing has full information." Moreover, it relies on the first person's inaccuracy in making a fair cut.
Answers.UserDisplayName: Rosie F
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-02-05T22:17:15.703Z
Answers.LastActivityDate: 2023-02-05T22:17:15.703Z
Answers.UserDisplayName: Brian Towers
Body: <p>It says on <a href="https://en.wikipedia.org/wiki/Fast_chess#Armageddon" rel="nofollow noreferrer">Wikipedia</a>:</p>
  <blockquote>
  <p>Some tournaments utilise a bidding system for individual players of each match to decide how little time they would be willing to play with as black. The player with the lowest bid for each match receives the black pieces with draw odds. This system minimises the perceived unfairness of Armageddon time controls that are decided in advance before a tournament with colours randomly allocated. Such an idea is reminiscent of the logical use case of fair cake-cutting.</p>
  </blockquote>
  <p>I haven't heard of <a href="https://en.wikipedia.org/wiki/Fair_cake-cutting" rel="nofollow noreferrer">fair cake-cutting</a> or more generally <a href="https://en.wikipedia.org/wiki/Fair_division" rel="nofollow noreferrer">fair division</a> before this. How is armageddon in chess like fair cake-cutting? Is bidding for lower time like bidding for a smaller quantity yet high quality slice of cake or something? Eg Smaller piece but has strawberry on it. So in this case:</p>
  <ul>
  <li><p>smaller piece = lower time + black</p>
  </li>
  <li><p>strawberry = draw odds</p>
  </li>
  </ul>
  <p>Quote:</p>
  <blockquote>
  <p>If a cake with a selection of toppings is simply cut into equal slices, different people will receive different amounts of its toppings, and some may not regard this as a fair division of the cake.</p>
  </blockquote>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-02-07T13:45:14.940Z
Comments.Text: Not a duplicate. It's a cross-post (even worse).
Comments.UserDisplayName: SecretAgentMan
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-02-07T14:10:01.060Z
Comments.Text: This has been asked and has an accepted answer on Math SE - https://math.stackexchange.com/questions/4623937/how-is-armageddon-in-chess-like-fair-cake-cutting-in-game-theory
Comments.UserDisplayName: Brian Towers
Tags: <tournament><time-control><armageddon>
Title: How is Armageddon in chess like fair cake-cutting in game theory?
ThreadText: # How is Armageddon in chess like fair cake-cutting in game theory?
  
  (Asked by: username_0 on 2023-02-05)
  
  It says on [Wikipedia](https://en.wikipedia.org/wiki/Fast_chess#Armageddon):
  
  > Some tournaments utilise a bidding system for individual players of each match to decide how little time they would be willing to play with as black. The player with the lowest bid for each match receives the black pieces with draw odds. This system minimises the perceived unfairness of Armageddon time controls that are decided in advance before a tournament with colours randomly allocated. Such an idea is reminiscent of the logical use case of fair cake-cutting.
  
  I haven't heard of [fair cake-cutting](https://en.wikipedia.org/wiki/Fair_cake-cutting) or more generally [fair division](https://en.wikipedia.org/wiki/Fair_division) before this. How is armageddon in chess like fair cake-cutting? Is bidding for lower time like bidding for a smaller quantity yet high quality slice of cake or something? Eg Smaller piece but has strawberry on it. So in this case:
  
  * smaller piece = lower time + black
  * strawberry = draw odds
  
  Quote:
  
  > If a cake with a selection of toppings is simply cut into equal slices, different people will receive different amounts of its toppings, and some may not regard this as a fair division of the cake.
  
  **Tags:** tournament, time-control, armageddon
  
  > **Comments:**
  > **username_1**: Not a duplicate. It's a cross-post (even worse).  
  > **username_2**: This has been asked and has an accepted answer on Math SE - https://math.stackexchange.com/questions/4623937/how-is-armageddon-in-chess-like-fair-cake-cutting-in-game-theory  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2023-02-05. Score: 2 | Accepted answer
  
  I have to admit I found the Wikipedia article on fair cake-cutting pretentious in the extreme. Why Lebesque Measure needs to be dragged into cutting a cake is beyond me despite being a mathematician who knows what Lebesgue measure is.
  
  Going back several decades to my university flat-sharing days, the standard solution to the pizza cutting problem (when we ordered a pizza take out to share between us) was that one person cut and the other person chose. When there were more than two of us the person cutting chose last. That way the person cutting had the motive to cut as evenly as possible.
  
  That's not quite analogous to the Armageddon colour choice problem. In cutting a cake or pizza the person choosing has full information. They can see exactly what the situation is. The chess colour choice is different. The second player doesn't know what the first player has bid. However both players can evaluate what the value is of playing black in relation to the other player and bid accordingly.
  
  What the two ways of choosing *do* have in common is that they both allow the players / eaters to judge their own best interests and choose, either a slice (to make with a knife or to eat) or a time, accordingly. That way none of the players / eaters can claim that the system was unfair to them, which players assigned black or white by chance might think.
  
  > **Comments:**
  > **username_0**: username_2♦ Is it wrong to think this way? 'smaller piece = lower time + black' but 'the strawberry on the smaller piece = draw odds' ? So you can have a smaller piece that is more delicious or a bigger piece that is less delicious. Quote on Wikipedia: 'If a cake with a selection of toppings is simply cut into equal slices, different people will receive different amounts of its toppings, and some may not regard this as a fair division of the cake.'  
  > **username_3**: "In cutting a cake or pizza the person choosing has full information." Moreover, it relies on the first person's inaccuracy in making a fair cut.  
  
  ---
  
  