Answers.Body: <p>The following is just my personal take on this, based on never having played hand-brain chess and on my extremely limited understanding of chess as a very weak player (chess.com ~1300 blitz, maybe ~1400 on a good day in classical). So take this with a grain of salt.</p>
  <p>I would think that if both players are relatively strong but one is clearly stronger (say an IM and a GM), the weaker of the two should be the hand and the stronger the brain. This is because the GM can likely trust that the IM would make the right move when given the piece to move. The IM would have a good enough understanding of the position to make the best move of the chosen piece.</p>
  <p>If one player is head and shoulders above the other, say someone like me and a strong rated player, then the weaker player should probably be the brain. I figure if I tell the strong player to move a piece, they'll manage to make the best of it. If I am the hand, I am more likely to make a mistake even if the stronger player gives me the right piece while if they are the hand, they would have a better chance of finding a good move even if I don't find the <em>best</em> move and suggest the <em>best</em> piece.</p>
  <p>If both players are relatively weak, I expect it makes no difference at all who is hand and who is brain.</p>
  
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Answers.Text: terdon, what do you think of my answer please? It's a little like yours, but I explain in terms of endgame vs middlegame and opening.
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Answers.Text: @BCLC um, OK. Good for you, I guess. I don't really know why you are asking for my opinion. As I said, I am not a strong player and I have absolutely no experience with hand/brain so my opinion seems quite useless to be honest.
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Answers.Text: terdon, we're about the same rating in chess/chess960
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Answers.Text: @BCLC sorry, I didn't mean to brush you off, I just don't really think my opinion is worth much since I don't know anything about hand/brain so my answer was just my random thoughts.
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Answers.Text: i know you're not brushing me off and that you're being humble, but your random thoughts got 11 upvotes and 0 downvotes. so i think more random thoughts/opinions from you re my answer will be helpful. basically i just think you're at least kinda right in re who should be hand/brain. i think stronger as brain will be more useful in the opening and middlegame (then again a lot of your 11 upvotes may have come from the hot network question thing)
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Answers.Text: also, i don't know anything about hand and brain either. i've seen only like a few games of it. but i think only a few games is all that one needs
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Answers.Text: also no [need to apologise](http://www.boredpanda.com/stop-saying-sorry-say-thank-you-comic-yao-xiao/)
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Answers.UserDisplayName: terdon
Answers.Body: <p>According to an <a href="http://talkchess.com/forum3/viewtopic.php?f=2&amp;t=79757&amp;sid=2ecb62f8f8c8dac4ceff85946f2a1023#p924933" rel="noreferrer">experiment</a> done on computers, it is preferable for the stronger team member to handle the <code>hand</code>.</p>
  
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Answers.Text: Maybe you could elaborate on the details of this experiment?
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Answers.Body: <p>(Note 1: A little similar to terdon's answer but with 3 stages in mind.)</p>
  <p>(Note 2: I got so mixed up with hand/brain. I prefer terminology move/piece. whatever. Anyway, I might've mistakenly mixed up hand/brain below even after proofreading.)</p>
  <hr />
  <p>I thought of chess/chess960 in terms of its 3 stages. Working backwards, I came up with the idea:</p>
  <blockquote>
  <p><strong>Brain</strong> stronger means advantage in <strong>opening or middlegame</strong>, but <strong>hand</strong> stronger means advantage in the <strong>endgame</strong>.</p>
  </blockquote>
  <p>Part I. <a href="https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp" rel="nofollow noreferrer">Positive</a> Part I (Here positive/normative is like <a href="https://law.stackexchange.com/questions/1375/what-is-the-opposite-of-argumentative">factual/argumentative</a>.)</p>
  <ol>
  <li><p>If you reach the <strong>endgame</strong>, then I think it's better if the stronger player was chosen to be <strong>hand</strong>.</p>
  </li>
  <li><p>Consider pawn endgames. The only possible things the hand could say are 'king' and 'pawn'.</p>
  </li>
  <li><p>Sometimes one should make a king move instead of a pawn move or vice-versa. However, very often it's obvious which one of king or pawn move, but it's long to calculate which move to make with the king/pawn to make. So, if one is a lot stronger, then we'd want to the stronger to be able to calculate it correctly as hand because otherwise the stronger's calculation ability is wasted on the obvious choices in the endgame.</p>
  </li>
  <li><p>Sometimes it's not obvious which to move between pawn or king, but <a href="https://en.wikipedia.org/wiki/Prior_probability" rel="nofollow noreferrer">a priori</a> this is 50/50. So, if hand is stronger, then assuming the brain is <em>good enough</em> to correctly calculate that in a certain pawn endgame which of king or pawn to move, then all we need do is let the hand carry the team by converting the winning endgame. (referred to in (9)).</p>
  </li>
  <li><p><strong>Another way to think of this is considering Samay Raina's dice chess</strong>/chess960 (eg <a href="https://www.youtube.com/watch?v=iETRRAlAelo" rel="nofollow noreferrer">this</a>): If 2 people play dice chess and somehow reach a pawn endgame, then it pretty much becomes normal chess/chess960 (because we roll until legal move). Basically, the fewer distinct pieces (I kind of assume that 'fewer distinct pieces' is synonymous to 'closer to endgame') in a game of dice chess/chess960 or hand and brain chess/chess960, then I think the closer we are to real chess/chess960.</p>
  </li>
  </ol>
  <p>Part II. <a href="https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp" rel="nofollow noreferrer">Positive</a> Part II</p>
  <ol start="6">
  <li><p>With Part I in mind: perhaps a certain team may choose as a strategy for the stronger player to be hand with the idea that 'if we get to endgame, then we will have an advantage.' Conversely/Obversely(/grammar?), the other team might pick the stronger player to be the <strong>brain</strong> hoping to get an advantage in the <strong>opening or middlegame</strong>.</p>
  </li>
  <li><p>What I understand here: As compared to the endgame, the opening or middlegame has a lot of distinct pieces, so it's more of <strong>which piece (brain)</strong> to move and less of <strong>which move (hand)</strong> to make with a given piece.</p>
  </li>
  </ol>
  <ul>
  <li><p>7.1. Eg for middlegame: load up some puzzle on lichess or chesstempo where you just got a piece captured and it's obvious you have to recapture but then you're not sure whether to retake a capture with knight, pawn or bishop. Let the stronger as brain calculate which piece and then let the weaker as hand do the obvious move given the piece told. I don't believe endgames are really like this though. I think of pawn endgames where you have to choose between retaking with, say, either or your f or your d pawn. Here, we want to let the weaker as hand to say the obvious piece and then let the stronger as brain to calculate which of the 2 pawns to recapture with. But of course choosing between 2 pawns can happen in opening or middlegame (see (11)).</p>
  </li>
  <li><p>7.2. Eg for opening: Well if brain says knight for the 1st move, then it's obviously going to be N(c/f)(3/6), so the hand doesn't really have to calculate here. It seems that generally there aren't going to be that much choices with pieces anyway like if hand previously played (g/b)(3/6) and brain says bishop, then perhaps brain means fianchetto.</p>
  </li>
  </ul>
  <p>Part III. <a href="https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp" rel="nofollow noreferrer">Normative</a> Part I</p>
  <ol start="8">
  <li>Ideally, the <strong>weaker as brain would be good enough to get through the opening and middlegame so that the stronger as hand could calculate for the endgame</strong>. If the weaker isn't good enough, then I guess let stronger be the brain. So <strong>for stronger as (not that much)/(that much) stronger, try stronger as, resp, brain/hand</strong>.</li>
  </ol>
  <ul>
  <li><p>8.1. For example, let's say we have teams of (1800,1400) and (2800,900). I think we'd want (1800,1400)=(hand,brain) but then (2800,900)=(brain,hand). Re the (2800,900)=(brain,hand): otherwise, the 2800 strength is wasted if the 900 can't figure out, say, if we should develop or castle. Forget endgame if you're not even going to make it past the middlegame or even the opening. I think we want to use the 2800 strength to get an advantage in middlegame or even opening. In the case of develop or castle, if the 2800 brain says 'king', then I guess the 900 hand isn't just going to move the king 1 square when castling is available.</p>
  </li>
  <li><p>8.2. For example, let's say we have teams of both (1800,1400). If one team does (1800,1400)=(brain,hand) while another does (1800,1400)=(hand,brain), then there seems to be a decent chance that they can make it to endgame, where the 1800 hand will almost surely crush the 1400 hand.</p>
  </li>
  </ul>
  <ol start="9">
  <li>Of course the stronger hand's advantage in the endgame depends on how few distinct pieces there are. Like if we reduce distinct pieces from 6 to 2 (eg pawn endgame), then great! But if it's 3 distinct eg rook endgame, then of course our a priori drops from 50% to 33% (see (4)).</li>
  </ol>
  <p>Part IV. (Bonus) <a href="https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp" rel="nofollow noreferrer">Normative</a> Part II: Playing strategy after the hand and brain are chosen.</p>
  <ol start="10">
  <li>I think what happens is the team with the stronger as hand/brain is going to try as much as possible to, resp, (get)/(not get) into endgame eg, resp, (make a lot of)/(avoid) trades, in particular (to trade)/(avoid trading) <a href="https://chess.stackexchange.com/questions/35503/why-is-there-association-between-a-queenless-position-and-the-endgame">queens</a>.</li>
  </ol>
  <ul>
  <li><p>10.1 I think this applies even if you don't adopt the above choice strategy. Say (2800,900)=(hand,brain)=(1800,1400). I guess it's not likely they'll end up in endgame assuming what I said above is correct, but if ever the (2800,900) really chooses or has to play as such, then I think they'll try to make a lot of trades or something.</p>
  </li>
  <li><p>10.1.1. However!!! The (hand,brain)=(1800,1400) team knowing this might have to adjust their playing strategy, but maybe it's still better for them to indeed choose (hand,brain)=(1800,1400).</p>
  </li>
  </ul>
  <ol start="11">
  <li>Adopting the above choice strategy, I think what the (2800,900)=(brain,hand) might do is avoid situations where they have to decide, like, between 2 pawns or 2 knights to recapture and also avoid trades as much as possible (see (7.1)).</li>
  </ol>
  <hr />
  <p>Maybe related: <a href="https://chess.stackexchange.com/questions/21828/is-a-team-of-gms-stronger-than-a-single-super-gm/36754#36754">Is a team of GMs stronger than a single super-GM?</a></p>
  
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Answers.Body: <p>Not a definitive answer, but I'm posting my comment based on the upvotes it received.</p>
  <p><strong>It depends.</strong> GMs have different opinions.</p>
  <p>GM Hikaru Nakamura has said it really depends on the situation. Additionally, he has commented that when the Brain, he often suggests moves that aren't correct because he is factoring in the likely Hand response to his move.</p>
  <p>GM Aman Hambleton stated the stronger ELO player should be the Hand generally because they will find good moves in most cases, and be able to identify a plan for a position much easier.</p>
  
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Answers.Text: Do you have links or citations for those GM statements?
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Answers.Text: @Pureferret Great point.  Both statements were made on their Twitch streams...it will take a lot of time to go through their collective 5 Youtube channels and their Twitch VODs to find these clips.  If I find them, I'll edit to include the links as citations.
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Answers.Text: SecretAgentMan and @Pureferret what do you think of my answer please? It's a little like terdon's, but I explain in terms of endgame vs middlegame and opening.
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Answers.Text: @BCLC I'm happy to comment on your answer.  To keep the page clean, I suggest you make a chat room and ping me with the link if you want to discuss.
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Body: <p>Exactly what it says on the tin, as the British say:</p>
  <blockquote>
  <p>In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?</p>
  </blockquote>
  <p>And secondarily:</p>
  <blockquote>
  <p>Is the answer to the previous question affected at all by the particular relative strengths of the players (as in, is the answer for a team involving Magnus Carlsen and I (probably around 1200) substantially different than that for team involving a 1600 and an 1800)?</p>
  </blockquote>
  <p>I can think of good reasons for both: the stronger player being the hand might be nice because they could select the best move under some constraints, and thus only very rarely make an outright blunder (generally, the only way they could play an outright blunder (assuming they're strong enough to pretty reliably avoid blunders) would be is a piece was chosen that had NO good moves, which I think is probably pretty rare). On the other hand, a stronger player being the brain might be preferred, as they could narrow down a decision tree for the lesser player in the hopes that the best move might become easier to see without such a large tree to analyze.</p>
  <p>To be clear, Hand and Brain chess is a type of team chess in which two players play each side. One (the &quot;Brain&quot;) is only allowed to pick a piece type to be moved, and the other (the &quot;Hand&quot;) must move that piece type without knowledge of what the first player intended. For example, if the &quot;Brain&quot; says &quot;pawn&quot;, then the &quot;Hand&quot; must move one of the pawns. If the &quot;Brain&quot; says &quot;king&quot;, then the &quot;Hand&quot; must move the king (includes castling).</p>
  
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Comments.Text: This is a hard question to answer because **playing Hand and Brain is a skill** (for the stronger player). That is, a team's joint playing strength is not a function of just the player's individual playing strengths but also the stronger player's ability to tune his playstyle and move choice.
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Comments.Text: @MobeusZoom do you disagree with my answer?
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Comments.Text: @BCLC you definitely make some interesting points! Do they explain all/most of Hand & Brain game results? You could have a look at some of the recent streamer games (the tournament Nakamura won earlier this year; the match between Carlsen + Ludwig vs Botez sisters) and see if the results tie up with your description and mistakes were where you expect them.
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Comments.Text: @MobeusZoom hehe i actually have no idea in terms of statistical/practical/a posteriori evaluation of my theory/hypothesis. i've seen just a few hand and brain matches and then formulated my theory/hypothesis mostly a priori
Comments.UserDisplayName: BCLC
Tags: <chess-variants>
Title: In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?
ThreadText: # In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?
  
  (Asked by: username_0 on 2021-05-05)
  
  Exactly what it says on the tin, as the British say:
  
  > In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?
  
  And secondarily:
  
  > Is the answer to the previous question affected at all by the particular relative strengths of the players (as in, is the answer for a team involving Magnus Carlsen and I (probably around 1200) substantially different than that for team involving a 1600 and an 1800)?
  
  I can think of good reasons for both: the stronger player being the hand might be nice because they could select the best move under some constraints, and thus only very rarely make an outright blunder (generally, the only way they could play an outright blunder (assuming they're strong enough to pretty reliably avoid blunders) would be is a piece was chosen that had NO good moves, which I think is probably pretty rare). On the other hand, a stronger player being the brain might be preferred, as they could narrow down a decision tree for the lesser player in the hopes that the best move might become easier to see without such a large tree to analyze.
  
  To be clear, Hand and Brain chess is a type of team chess in which two players play each side. One (the "Brain") is only allowed to pick a piece type to be moved, and the other (the "Hand") must move that piece type without knowledge of what the first player intended. For example, if the "Brain" says "pawn", then the "Hand" must move one of the pawns. If the "Brain" says "king", then the "Hand" must move the king (includes castling).
  
  **Tags:** chess-variants
  
  > **Comments:**
  > **username_1**: This is a hard question to answer because **playing Hand and Brain is a skill** (for the stronger player). That is, a team's joint playing strength is not a function of just the player's individual playing strengths but also the stronger player's ability to tune his playstyle and move choice.  
  > **username_2**: @MobeusZoom do you disagree with my answer?  
  > **username_1**: @username_2 you definitely make some interesting points! Do they explain all/most of Hand & Brain game results? You could have a look at some of the recent streamer games (the tournament Nakamura won earlier this year; the match between Carlsen + Ludwig vs Botez sisters) and see if the results tie up with your description and mistakes were where you expect them.  
  > **username_2**: @MobeusZoom hehe i actually have no idea in terms of statistical/practical/a posteriori evaluation of my theory/hypothesis. i've seen just a few hand and brain matches and then formulated my theory/hypothesis mostly a priori  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_6 on 2021-05-05. Score: 12 | Accepted answer
  
  Not a definitive answer, but I'm posting my comment based on the upvotes it received.
  
  **It depends.** GMs have different opinions.
  
  GM Hikaru Nakamura has said it really depends on the situation. Additionally, he has commented that when the Brain, he often suggests moves that aren't correct because he is factoring in the likely Hand response to his move.
  
  GM Aman Hambleton stated the stronger ELO player should be the Hand generally because they will find good moves in most cases, and be able to identify a plan for a position much easier.
  
  > **Comments:**
  > **username_7**: Do you have links or citations for those GM statements?  
  > **username_6**: @Pureferret Great point.  Both statements were made on their Twitch streams...it will take a lot of time to go through their collective 5 Youtube channels and their Twitch VODs to find these clips.  If I find them, I'll edit to include the links as citations.  
  > **username_2**: username_6 and @Pureferret what do you think of my answer please? It's a little like username_3's, but I explain in terms of endgame vs middlegame and opening.  
  > **username_6**: @username_2 I'm happy to comment on your answer.  To keep the page clean, I suggest you make a chat room and ping me with the link if you want to discuss.  
  
  ---
  
  ### Answer by username_3 on 2021-05-06. Score: 11
  
  The following is just my personal take on this, based on never having played hand-brain chess and on my extremely limited understanding of chess as a very weak player (chess.com ~1300 blitz, maybe ~1400 on a good day in classical). So take this with a grain of salt.
  
  I would think that if both players are relatively strong but one is clearly stronger (say an IM and a GM), the weaker of the two should be the hand and the stronger the brain. This is because the GM can likely trust that the IM would make the right move when given the piece to move. The IM would have a good enough understanding of the position to make the best move of the chosen piece.
  
  If one player is head and shoulders above the other, say someone like me and a strong rated player, then the weaker player should probably be the brain. I figure if I tell the strong player to move a piece, they'll manage to make the best of it. If I am the hand, I am more likely to make a mistake even if the stronger player gives me the right piece while if they are the hand, they would have a better chance of finding a good move even if I don't find the *best* move and suggest the *best* piece.
  
  If both players are relatively weak, I expect it makes no difference at all who is hand and who is brain.
  
  > **Comments:**
  > **username_2**: username_3, what do you think of my answer please? It's a little like yours, but I explain in terms of endgame vs middlegame and opening.  
  > **username_3**: @username_2 um, OK. Good for you, I guess. I don't really know why you are asking for my opinion. As I said, I am not a strong player and I have absolutely no experience with hand/brain so my opinion seems quite useless to be honest.  
  > **username_2**: username_3, we're about the same rating in chess/chess960  
  > **username_3**: @username_2 sorry, I didn't mean to brush you off, I just don't really think my opinion is worth much since I don't know anything about hand/brain so my answer was just my random thoughts.  
  > **username_2**: i know you're not brushing me off and that you're being humble, but your random thoughts got 11 upvotes and 0 downvotes. so i think more random thoughts/opinions from you re my answer will be helpful. basically i just think you're at least kinda right in re who should be hand/brain. i think stronger as brain will be more useful in the opening and middlegame (then again a lot of your 11 upvotes may have come from the hot network question thing)  
  > **username_2**: also, i don't know anything about hand and brain either. i've seen only like a few games of it. but i think only a few games is all that one needs  
  > **username_2**: also no [need to apologise](http://www.boredpanda.com/stop-saying-sorry-say-thank-you-comic-yao-xiao/)  
  
  ---
  
  ### Answer by username_4 on 2022-04-26. Score: 5
  
  According to an [experiment](http://talkchess.com/forum3/viewtopic.php?f=2&t=79757&sid=2ecb62f8f8c8dac4ceff85946f2a1023#p924933) done on computers, it is preferable for the stronger team member to handle the `hand`.
  
  > **Comments:**
  > **username_5**: Maybe you could elaborate on the details of this experiment?  
  
  ---
  
  ### Answer by username_2 on 2021-08-06. Score: 1
  
  (Note 1: A little similar to username_3's answer but with 3 stages in mind.)
  
  (Note 2: I got so mixed up with hand/brain. I prefer terminology move/piece. whatever. Anyway, I might've mistakenly mixed up hand/brain below even after proofreading.)
  
  ---
  
  I thought of chess/chess960 in terms of its 3 stages. Working backwards, I came up with the idea:
  
  > **Brain** stronger means advantage in **opening or middlegame**, but **hand** stronger means advantage in the **endgame**.
  
  Part I. [Positive](https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp) Part I (Here positive/normative is like [factual/argumentative](https://law.stackexchange.com/questions/1375/what-is-the-opposite-of-argumentative).)
  
  1. If you reach the **endgame**, then I think it's better if the stronger player was chosen to be **hand**.
  2. Consider pawn endgames. The only possible things the hand could say are 'king' and 'pawn'.
  3. Sometimes one should make a king move instead of a pawn move or vice-versa. However, very often it's obvious which one of king or pawn move, but it's long to calculate which move to make with the king/pawn to make. So, if one is a lot stronger, then we'd want to the stronger to be able to calculate it correctly as hand because otherwise the stronger's calculation ability is wasted on the obvious choices in the endgame.
  4. Sometimes it's not obvious which to move between pawn or king, but [a priori](https://en.wikipedia.org/wiki/Prior_probability) this is 50/50. So, if hand is stronger, then assuming the brain is *good enough* to correctly calculate that in a certain pawn endgame which of king or pawn to move, then all we need do is let the hand carry the team by converting the winning endgame. (referred to in (9)).
  5. **Another way to think of this is considering Samay Raina's dice chess**/chess960 (eg [this](https://www.youtube.com/watch?v=iETRRAlAelo)): If 2 people play dice chess and somehow reach a pawn endgame, then it pretty much becomes normal chess/chess960 (because we roll until legal move). Basically, the fewer distinct pieces (I kind of assume that 'fewer distinct pieces' is synonymous to 'closer to endgame') in a game of dice chess/chess960 or hand and brain chess/chess960, then I think the closer we are to real chess/chess960.
  
  Part II. [Positive](https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp) Part II
  
  6. With Part I in mind: perhaps a certain team may choose as a strategy for the stronger player to be hand with the idea that 'if we get to endgame, then we will have an advantage.' Conversely/Obversely(/grammar?), the other team might pick the stronger player to be the **brain** hoping to get an advantage in the **opening or middlegame**.
  7. What I understand here: As compared to the endgame, the opening or middlegame has a lot of distinct pieces, so it's more of **which piece (brain)** to move and less of **which move (hand)** to make with a given piece.
  
  * 7.1. Eg for middlegame: load up some puzzle on lichess or chesstempo where you just got a piece captured and it's obvious you have to recapture but then you're not sure whether to retake a capture with knight, pawn or bishop. Let the stronger as brain calculate which piece and then let the weaker as hand do the obvious move given the piece told. I don't believe endgames are really like this though. I think of pawn endgames where you have to choose between retaking with, say, either or your f or your d pawn. Here, we want to let the weaker as hand to say the obvious piece and then let the stronger as brain to calculate which of the 2 pawns to recapture with. But of course choosing between 2 pawns can happen in opening or middlegame (see (11)).
  * 7.2. Eg for opening: Well if brain says knight for the 1st move, then it's obviously going to be N(c/f)(3/6), so the hand doesn't really have to calculate here. It seems that generally there aren't going to be that much choices with pieces anyway like if hand previously played (g/b)(3/6) and brain says bishop, then perhaps brain means fianchetto.
  
  Part III. [Normative](https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp) Part I
  
  8. Ideally, the **weaker as brain would be good enough to get through the opening and middlegame so that the stronger as hand could calculate for the endgame**. If the weaker isn't good enough, then I guess let stronger be the brain. So **for stronger as (not that much)/(that much) stronger, try stronger as, resp, brain/hand**.
  
  * 8.1. For example, let's say we have teams of (1800,1400) and (2800,900). I think we'd want (1800,1400)=(hand,brain) but then (2800,900)=(brain,hand). Re the (2800,900)=(brain,hand): otherwise, the 2800 strength is wasted if the 900 can't figure out, say, if we should develop or castle. Forget endgame if you're not even going to make it past the middlegame or even the opening. I think we want to use the 2800 strength to get an advantage in middlegame or even opening. In the case of develop or castle, if the 2800 brain says 'king', then I guess the 900 hand isn't just going to move the king 1 square when castling is available.
  * 8.2. For example, let's say we have teams of both (1800,1400). If one team does (1800,1400)=(brain,hand) while another does (1800,1400)=(hand,brain), then there seems to be a decent chance that they can make it to endgame, where the 1800 hand will almost surely crush the 1400 hand.
  
  9. Of course the stronger hand's advantage in the endgame depends on how few distinct pieces there are. Like if we reduce distinct pieces from 6 to 2 (eg pawn endgame), then great! But if it's 3 distinct eg rook endgame, then of course our a priori drops from 50% to 33% (see (4)).
  
  Part IV. (Bonus) [Normative](https://www.investopedia.com/ask/answers/12/difference-between-positive-normative-economics.asp) Part II: Playing strategy after the hand and brain are chosen.
  
  10. I think what happens is the team with the stronger as hand/brain is going to try as much as possible to, resp, (get)/(not get) into endgame eg, resp, (make a lot of)/(avoid) trades, in particular (to trade)/(avoid trading) [queens](https://chess.stackexchange.com/questions/35503/why-is-there-association-between-a-queenless-position-and-the-endgame).
  
  * 10.1 I think this applies even if you don't adopt the above choice strategy. Say (2800,900)=(hand,brain)=(1800,1400). I guess it's not likely they'll end up in endgame assuming what I said above is correct, but if ever the (2800,900) really chooses or has to play as such, then I think they'll try to make a lot of trades or something.
  * 10.1.1. However!!! The (hand,brain)=(1800,1400) team knowing this might have to adjust their playing strategy, but maybe it's still better for them to indeed choose (hand,brain)=(1800,1400).
  
  11. Adopting the above choice strategy, I think what the (2800,900)=(brain,hand) might do is avoid situations where they have to decide, like, between 2 pawns or 2 knights to recapture and also avoid trades as much as possible (see (7.1)).
  
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  Maybe related: [Is a team of GMs stronger than a single super-GM?](https://chess.stackexchange.com/questions/21828/is-a-team-of-gms-stronger-than-a-single-super-gm/36754#36754)
  
  
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