PT147 · S4 · Q25 One way to compare chess-playing

While this answer seems reasonable, since it's reinforcing the "more moves examined = better chance of winning" connection, we don't know how to compare these two different programs. It's not like the passage told us that the only thing that affects chance of winning is number of possible moves examined in the time constraint. Two different chess-playing programs have been designed by two different (groups of) computer programmers. We have no idea what other aspects of designing a chess program are important. Maybe Eddie's chess program can consider more possible moves than Sharon's chess program, but Eddie didn't give good instructions to his chess-playing algorithm for what to make of all those possible moves considered. He might have better raw materials (more data for the computer to consider when selecting the next move) but less wisdom in terms of selecting the best move on the basis of that richer data. Since the program that considers more possible moves might be terrible when it comes to strategically picking the best of those possible moves, it might still be less likely to win than the other chess program. The correct answer is pretty similar to this one, but the correct answer hedges its prediction, making it safer language. It says "in general, the program considering more moves will have a better chance". This answer says, "the program considering more moves will have a better chance".

We have no support for this strong claim. There could easily be older computers with slow processing speeds that are too slow for certain chess programs to run on them. The author even seemed to allow for this possibility by saying, "Given any two computers with which a chess-playing program is compatible", implying that there may be some computers with which a given chess-playing program is not compatible.

We weren't really given any way to judge a comparison between two different chess-playing programs. In this head-to-head between program A and program B, we can say that program B is running on the faster computer. Does that guarantee that program B will consider more possible moves in the allotted time? No, because we don't know about design differences between program A and program B. Perhaps program B was written with really inefficient coding, so it takes more processing time/energy for B to consider a possible move than it does for A to consider a move. Since the design of the program could have such a difference on the performance efficiency of the program, we can't automatically say that any chess program on a faster program will consider more moves than any chess program on a slower computer.

There probably is some break even point, where you offset the superior computer speed of one computer with a smaller time limit per move, so that Program A is able to calculate the same number of possible moves whether it gets 5 seconds on the slower computer or 4 seconds on the faster computer. But the ratio of time limits would have to match the inverse ratio of computer processing speeds. This answer choice is not dialing in the mathematical specificity it would take to end up with an equal (i.e. identical) chance of winning. It's simply saying, "if you give the program on the slower computer more time to examine possible moves, it'll be equal chance". Maybe if we give it an extra 0.5 seconds it's not enough extra time to consider an equal number of possible moves. Maybe if we give it an extra 20 seconds, then the program on the slower computer is now considering way more possible moves.