user3325: Is there any material difference between chess the way it is now versus doing away with check and checkmate and defining victory as simply capturing the opponent's King, assuming an available King capture is always taken?
Here is another way way of putting it, along with the motivation for my question: If a chess AI ignored the concepts of check and checkmate, and treated the material value of a King as infinity, would that change its behavior?

user4362: Apart from stalemate, what you have to account for is the possibility that both kings are captured in succession, restoring the balance. That's what one of my chess programs did, capturing a defended piece with the king, because the defending pawn was pinned against my king. 
So, if the only possible moves are with the king, you need to check whether those are actually legal, or whether the position is stalemate. And when a king is taken, you need to make sure that subsequent moves don't change the evaluation. Apart from that you need to check for checkmate only in the current position, as far as I can see. 

user8201: This variant is distinct from regular chess. Some positions you can win more quickly, and others more slowly. This comes about because stalemate is still a thing.

[title "White to move. (a) mate in 3 moves (b) unroyal: capture king in 2 moves"]  
[fen "7k/5P2/8/5K2/8/8/8/8 w - - 0 1"]  


Solution:
(a) 1. Kf6 Kh7 2. f8=R Kh6 3. Rh8#
(b) 1. Kg6 Kg8,Kg7,Kh7 2. fxKg8,KxKg7,KxKh7

[title "White to move. (a) mate in 1 move (b) unroyal: capture king in 3 moves"]  
[fen "8/8/8/5N2/K7/8/4p1pp/4Bbrk w - - 0 1"]  


Solution:
(a) 1. Ng3#
(b) 1. Bf2 e1=? 2. Ng3 ~ 3. NxKh1
By the way, does anyone here know a name for this variant of chess where there are no checks or checkmates, and you win by capturing the opponent's king? I'm calling it Unroyal Chess for the purposes of this post. "Checkless chess" is something different. It means that check is illegal unless it ends the game with checkmate.

user2299: Your "checkless" chess AI would run into problems with the stalemate rule. It would consider the poaition with white king on a6, white pawn a7, black king a8, a win for White because wherever Black moves his king it will get captured. In standard chess, of course, the position is a draw.

3325: <p>Is there any material difference between chess the way it is now versus doing away with check and checkmate and defining victory as simply capturing the opponent's King, assuming an available King capture is always taken?</p>

<p>Here is another way way of putting it, along with the motivation for my question: If a chess AI ignored the concepts of check and checkmate, and treated the material value of a King as infinity, would that change its behavior?</p>
 4362: <p>Apart from stalemate, what you have to account for is the possibility that both kings are captured in succession, restoring the balance. That's what one of my chess programs did, capturing a defended piece with the king, because the defending pawn was pinned against my king. </p>

<p>So, if the only possible moves are with the king, you need to check whether those are actually legal, or whether the position is stalemate. And when a king is taken, you need to make sure that subsequent moves don't change the evaluation. Apart from that you need to check for checkmate only in the current position, as far as I can see. </p>
 8201: <p>This variant is distinct from regular chess. Some positions you can win more quickly, and others more slowly. This comes about because stalemate is still a thing.</p>

<pre><code>
[title "White to move. (a) mate in 3 moves (b) unroyal: capture king in 2 moves"]  
[fen "7k/5P2/8/5K2/8/8/8/8 w - - 0 1"]  

</code></pre>

<p>Solution:<br>
(a) 1. Kf6 Kh7 2. f8=R Kh6 3. Rh8#<br>
(b) 1. Kg6 Kg8,Kg7,Kh7 2. fxKg8,KxKg7,KxKh7</p>

<pre><code>
[title "White to move. (a) mate in 1 move (b) unroyal: capture king in 3 moves"]  
[fen "8/8/8/5N2/K7/8/4p1pp/4Bbrk w - - 0 1"]  

</code></pre>

<p>Solution:<br>
(a) 1. Ng3#<br>
(b) 1. Bf2 e1=? 2. Ng3 ~ 3. NxKh1</p>

<p>By the way, does anyone here know a name for this variant of chess where there are no checks or checkmates, and you win by capturing the opponent's king? I'm calling it Unroyal Chess for the purposes of this post. "Checkless chess" is something different. It means that check is illegal <em>unless</em> it ends the game with checkmate.</p>
 2299: <p>Your "checkless" chess AI would run into problems with the stalemate rule. It would consider the poaition with white king on a6, white pawn a7, black king a8, a win for White because wherever Black moves his king it will get captured. In standard chess, of course, the position is a draw.</p>
