user19521: I'm reading Kasparov's Deep Thinking and I came across this sentence:

In one computer championship, a machine blundered a full piece early
in the game but its opponent declined to capture it.

When I googled it I also saw the term "half piece" but couldn't find any definition on any of them.
I'm not a native speaker and I'm not familiar with chess terms in English. I'm guessing full piece is an important piece such as queen or rook and half piece is a minor piece like bishop or knight but I want to be sure. Can you explain what they mean?

user19534: I do not know. In my circles, the bishop and knight are not always "equal" to exactly 3 pawns when they are being exchanged.  
For us, we might say a player is "a half-piece down" after a bishop for knight exchange (if material was otherwise equal), or vice versa (depending on when the exchange happens), or even "three and a half down" if the player blunders their higher valued minor piece.
In this scheme, at the start of a game, a knight may be considered worth more than a bishop (3.5 while the bishop is 3); while later on, the values switch and the bishop becomes worth more (3.5 while knight becomes 3). Thus, in total evaluation, you get a "half piece" difference.
Of course, this is generally only considered when a bishop for knight or knight for bishop is exchanged, or a minor piece is sacrificed or blundered; or perhaps when evaluating the strength of positions at the end game (as some folks may consider the bishops more useful in the end. But I'd say, the positioning determines which would be better in any situation.
It is worth reading this Atlantic article for the general idea. 
Addtionally, the the Wiki page notes many material valuation considerations and alternatives that include fractional pieces.

user12523: I don't think "full piece" means anything beyond "piece" but "full" was added for emphasis. This is to highlight the magnitude of the blunder, since many blunders are smaller than a piece; for example, one can blunder a pawn or the Exchange (rook for knight or bishop), or trade a piece for a pawn or two.
The commonly used terms to distinguish queen/rook vs bishop/knight are major piece and minor piece. You may also see "heavy piece" used as a synonym for major piece.
The term "half-piece" doesn't make a lot of sense and I had never heard it. Using Google I found a couple of examples but they are in the context of chess variants such as "inchworm chess", where a piece can be in two squares at once (half a piece on each square), or "symmetric unirexal chess", where two "half pieces" can occupy the same square.
Let's elaborate on the statement above that many blunders are "less than a piece". In the best-known piece value scheme, minor pieces are worth three pawns, rooks are worth five pawns, and queens are worth nine pawns. The quote about blundering a "full piece" probably referred to a minor piece, because otherwise it would say "blundered a rook" or "blundered the queen". Therefore blundering a pawn would be like blundering one-third of a piece, and the Exchange would be two-thirds (a piece for a pawn would be two-thirds, too). Note that there is no way to blunder "half a piece" under this value scheme. (Note however that these values are just a rough guideline!)

user13433: 
blundering a full piece

or

being a full piece down

are typical expressions in English chess literature.
With the little word "full", the author wants to make clear that the player has not only lost the piece, but that they also received no consolation material in return, i.e. one or two pawns. An alternative expression is "blundering a clean piece" / "being a clean piece down".
The typical scale is:

The opponent blundered/sacrificed a piece for two pawns.
The opponent blundered/sacrificed a piece for a pawn.
The opponent blundered/sacrificed a full/clean piece.

("Sacrifice" or "blunder" generally depend on the positional compensation for the loss of the piece.)
The "piece" in question may theoretically be a any of the "pieces" knight, bishop, rook or queen (pawns are not "pieces" and the king cannot be captured), but typically you would expect it to be either a knight or a bishop (in the other cases it would rather be e.g. "being a full rook down" or "being a full queen down").
The term "half piece" does not exist, at least to my knowledge.

19521: <p>I'm reading Kasparov's Deep Thinking and I came across this sentence:</p>
<blockquote>
<p>In one computer championship, a machine blundered a full piece early
in the game but its opponent declined to capture it.</p>
</blockquote>
<p>When I googled it I also saw the term &quot;half piece&quot; but couldn't find any definition on any of them.</p>
<p>I'm not a native speaker and I'm not familiar with chess terms in English. I'm guessing full piece is an important piece such as queen or rook and half piece is a minor piece like bishop or knight but I want to be sure. Can you explain what they mean?</p>
 19534: <p>I do not know. In my circles, the bishop and knight are not always "equal" to exactly 3 pawns when they are being exchanged.  </p>

<p>For us, we might say a player is "a half-piece down" after a bishop for knight exchange (if material was otherwise equal), or vice versa (depending on when the exchange happens), or even "three and a half down" if the player blunders their higher valued minor piece.</p>

<p>In this scheme, at the start of a game, a knight may be considered worth <em>more</em> than a bishop (3.5 while the bishop is 3); while later on, the values switch and the bishop becomes worth more (3.5 while knight becomes 3). Thus, in total evaluation, you get a "half piece" difference.</p>

<p>Of course, this is generally only considered when a bishop for knight or knight for bishop is exchanged, or a minor piece is sacrificed or blundered; or perhaps when evaluating the strength of positions at the end game (as some folks may consider the bishops more useful in the end. But I'd say, the positioning determines which would be better in any situation.</p>

<p>It is worth reading <a href="https://www.theatlantic.com/entertainment/archive/2014/11/knight-vs-bishop/383202/" rel="nofollow noreferrer">this Atlantic article</a> for the general idea. </p>

<p>Addtionally, the the <a href="https://en.wikipedia.org/wiki/Chess_piece_relative_value" rel="nofollow noreferrer">Wiki</a> page notes many material valuation considerations and alternatives that include fractional pieces.</p>
 12523: <p>I don't think "full piece" means anything beyond "piece" but "full" was added for emphasis. This is to highlight the magnitude of the blunder, since many blunders are smaller than a piece; for example, one can blunder a pawn or the Exchange (rook for knight or bishop), or trade a piece for a pawn or two.</p>

<p>The commonly used terms to distinguish queen/rook vs bishop/knight are <strong>major piece</strong> and <strong>minor piece</strong>. You may also see "heavy piece" used as a synonym for major piece.</p>

<p>The term "half-piece" doesn't make a lot of sense and I had never heard it. Using Google I found a couple of examples but they are in the context of chess variants such as "<a href="https://www.chessvariants.com/diffmove.dir/inchworm-chess.html" rel="noreferrer">inchworm chess</a>", where a piece can be in two squares at once (half a piece on each square), or "<a href="https://www.chessvariants.com/rules/symmetric-unirexal-chess" rel="noreferrer">symmetric unirexal chess</a>", where two "half pieces" can occupy the same square.</p>

<p>Let's elaborate on the statement above that many blunders are "less than a piece". In the best-known piece value scheme, minor pieces are worth three pawns, rooks are worth five pawns, and queens are worth nine pawns. The quote about blundering a "full piece" probably referred to a minor piece, because otherwise it would say "blundered a rook" or "blundered the queen". Therefore blundering a pawn would be like blundering one-third of a piece, and the Exchange would be two-thirds (a piece for a pawn would be two-thirds, too). Note that there is no way to blunder "half a piece" under this value scheme. (Note however that these values are just a rough guideline!)</p>
 13433: <blockquote>
<p>blundering a <strong>full</strong> piece</p>
</blockquote>
<p>or</p>
<blockquote>
<p>being a <strong>full</strong> piece down</p>
</blockquote>
<p>are typical expressions in English chess literature.</p>
<p>With the little word &quot;<strong>full</strong>&quot;, the author wants to make clear that the player has not only lost the piece, but that they also received no consolation material in return, i.e. one or two pawns. An alternative expression is &quot;blundering a <strong>clean</strong> piece&quot; / &quot;being a <strong>clean</strong> piece down&quot;.</p>
<p>The typical scale is:</p>
<blockquote>
<p>The opponent blundered/sacrificed a piece for two pawns.</p>
<p>The opponent blundered/sacrificed a piece for a pawn.</p>
<p>The opponent blundered/sacrificed a full/clean piece.</p>
</blockquote>
<p>(&quot;Sacrifice&quot; or &quot;blunder&quot; generally depend on the positional compensation for the loss of the piece.)</p>
<p>The &quot;piece&quot; in question may theoretically be a any of the &quot;pieces&quot; knight, bishop, rook or queen (pawns are not &quot;pieces&quot; and the king cannot be captured), but typically you would expect it to be either a knight or a bishop (in the other cases it would rather be e.g. &quot;being a full rook down&quot; or &quot;being a full queen down&quot;).</p>
<p>The term &quot;<strong>half</strong> piece&quot; does not exist, at least to my knowledge.</p>
