One way to compare chess-playing programs is to compare how they perform with fixed time limits per move. Given any t...

Irina on August 27, 2019

@chelseaborg,

The stimulus talks about the same program running on two different computers, whereas (A) requires us to infer the chances of winning for two different programs run on the same computer. We cannot make this inference since the premises differ from the ones in the stimulus.

Let me know if you have any further questions.

Vanessa-Gomez on April 6, 2020

Can you please explain why the first sentence "One way to compare chess-playing programs is to compare how they perform with fixed time limits per move." is not considered a comparison of different programs?

AneeshU on June 12, 2022

According to my understanding, A is saying that all other things being equal, the program which examines more moves will have a better chance at winning than another program. While its true that the stimulus talks about two different computers, running the programs on the same computer only means that speed of the computer is a non-factor for comparison. In addition, the justification given for the conclusion in the stimulus is that, "the program will be able to examine more possible moves in the time allotted per move". Since the programs cannot examine more possible moves because of better processing speed of the computer on which it is executed, one indication that a program is likely to win against another program is that the first program is designed to examine more possible moves in the same amount of time and processing speed.

What's the flaw in the logic above?

jakennedy on June 12, 2022

Hi @AneeshU,
I think the problem is with your first statement. The stimulus never says that the only consideration is the rate at which the program examines moves.

The stimulus states that “one way to compare chess-playing programs is to compare how they perform with fixed time limits per move”. It then goes on to explain that given any two computers, a chess-playing program will perform better on the faster computer. The key is that the stimulus is dealing with one program across two computers, whereas answer choice A is referring two different programs on the same computer.

I’ll give you a real-world example. When I was in college, I attempted to make a chess program, but it wasn’t very good. If my chess program were to run on a fast computer, it would undoubtedly have performed better than on a slow computer (analogous to what the stimulus said). However, if you were to put my chess program on a fast computer up against a world-class chess engine like Stockfish or AlphZero on a slow computer, my program would have lost every time (but answer choice A would suggest that mine should win simply because it is on a faster computer).

AneeshU on June 13, 2022

Hi Jacob,

The passage says "such a program will have a BETTER chance of winning on the faster computer. This is simply because the program will be able to examine more possible moves in the time allotted per move," which I took to mean

"faster computer" (arrow right) "examine more moves in allotted time" (arrow right) better chance of winning

If we take the second half, of this^, then we know that examining more moves in the allotted time means that the program has a better chance of winning. It's a non-factor whether this is the only consideration because we don't discuss whether the program will conclusively win in the stimulus or any of the options.

I agree that in the real world, we would not be able to say that one program was superior to the other based on the number of moves considered, however, the stimulus (and option A) clearly says that the program will have a BETTER chance of winning if it is able to examine more moves.

In addition, why is the real-world example that you gave not applicable to C? In option C, it is also possible that the program is up against a world class chess engine.

"C: In general, the more moves a given chess-playing program is able to examine under given time constraints per move, the better the chances that program will win."

jakennedy on June 15, 2022

Hi Aneesh,

You're right that the stimulus says that a program will have a better chance of winning on a faster computer because it can examine more possible moves, but the problem is, the stimulus is comparing a program on a slow computer with that SAME program on a faster computer. Of course, using the same program on a faster computer will lead to better results. The stimulus never asserts that the program in question will be faster than every other program in existence. In fact, the stimulus never compares that program with another program at all.

That is why answer choice C is correct. Like the stimulus, it is only focusing on one program ("a given chess playing program"). That program will have a better chance of winning than the SAME program would have had if it were to examine fewer moves.

My real-world example isn't applicable to C because, according to C, my inefficient program would be better if it could examine more moves per unit of time. That is true. While it would still be a bad program, it would be at least slightly better under those circumstances.

Answer choice A, on the other hand, would suggest that my bad program could beat an amazing program so long as it is on a faster computer.

See how A is comparing the program with a different program, whereas C is comparing a program with itself? That subtle difference is the key to the answer here.

To recap:
Answer choice A is saying that the program would have a better chance at winning than a different program

Answer choice C is saying the program would have a better chance at winning than that same program under different circumstances

I hope this helps. Let me know if you have other questions.

AneeshU on June 16, 2022

Thanks for explaining, Jacob. I'm clear now.

devon on April 4, 2023

I would value a direct answer to Vanessa's Q: "Can you please explain why the first sentence - 'One way to compare chess-playing programs is to compare how they perform with fixed time limits per move' - is not considered a comparison of different programs?"

Emil-Kunkin on April 9, 2023

Hi, a direct comparison would mean actually comparing two programs. It would have to mention two programs and actually compare them, e.g. "chess.com's engine is able to play to an ELO of 1600 with a 1 second time limit, while LI Chess' engine is only able to play to a an ELO of 1450.

The first sentence gives a criterion www can use to compare. This is not an actual comparison.