I think there's no difference here at all. In darts, it is very very clear what "perfect" play entails, however the physical act of achieving it is incredibly difficult. A darts match consists of two people attempting to come closer to that level of perfection, but in the end, both people will make "mistakes" (fall short), and the winner is the person who makes fewer mistakes. Identically, in chess there is presumably a "perfect play", which most people think would lead to a draw, but no human (or computer) is capable of achieving it yet. A chess game consists of two opponents striving to come as close to this level of perfection as possible, and if one person comes closer by a large enough margin they will win.

There are two reasons you perceive chess and darts as different. First, because in chess the perfect play remains unclear, so it's impossible to determine with certainty how far from perfection each competitor deviated, while in darts it's obvious: every time someone fails to hit the optimal spot with a throw they have made a mistake. Second, because darts is a physical pursuit, you're more prone to forgive the lack of perfection, and treat the winner as the person who "did better" rather than treat the loser as the person who "did worse", since we all have a lifetime of experience in exactly how impossible it is to perfectly control our bodies, yet we are all arrogant to think that mental perfection *should* be within our grasp.

Edit: And just to nitpick, shooting a course record in golf isn't "perfect play". Every time a shot doesn't go into the hole, it's clearly a mistake, in the sense of this discussion. The game theory optimal solution to golf is just to get a hole-in-one on every hole. (Sorry, this edit was a smart-ass comment, with no real bearing on the discussion, but I couldn't help myself )

Your opponent's mistake is then to not score a 147 (or at least win the frame) on his opening break next frame.

I agree though it's a bit ridiculous to talk about perfect play in snooker or golf, while in poker or chess it's at least conceivable.

How is this? I think both, golf and snooker, are infinitely more likely to be "solved" than chess. In snooker, a robot could analyze the board perfectly and shoot the perfect shot every single time. Humans' problem there isn't finding the best move, but executing it - something a robot would have zero difficulty with. And momentum + direction of a stick isn't exactly sophisticated robotics. Golf would certainly be much more challenging than snooker, but even there it's not a huge leap.

At my university, a team at the robotics lab was working on developing a team of soccer playing bots. Trust me, snooker and golf would be rapidly solved if there was any interest in it. But who wants to see a world champion get crushed by some goofy looking calculating robotic box? Let's reserve that for the 'mental' games for whatever reason.

I really liked you post BobJoeJim.

I would now hold that mistakes occur in these games as well and still hold that all wins are marred by the fact the opponent makes a mistake and their aesthetic value is not as pleasing as producing something which is great without the recourse to someone else's failing. But I guess only the creation of works of art would satisfy that criterion. I guess I am saying the search for aesthetic beauty in chess/checkers is marred by definition.

I am surprised that robotics is this well developed. What has happened to building a domestic robot to do household chores?

Oddly enough, household chores are actually a whole lot more challenging than playing snooker perfectly since the rules and objectives are not well defined. So I guess you could always become a butler for true aesthetic pleasure?

I laughed out loud. I really did. Thank you.

While most shots would be trivially easy for a robot, snooker is chaotic when you have situations involving many balls in close contact. A tiny difference in the angle or power of your shot, or a tiny imperfection in the felt that may exist even on a professional-quality table, can lead to an enormous difference in the shot's result.

I don't think there exist sophisticated enough robotics to hit a golf-hole sized target at 500 yards, even if you could launch the ball from a cannon instead of swinging a horribly inefficient golf club. But I actually think that problem might be easier to solve.

Many balls in close contact aren't particularly difficult to simulate! The math/physics is actually pretty simple. And you can even compensate for invisible imperfections in the table. Just measure the frictional/resistance values with a range and then determine the EV with a range of resistance for whatever delta you want (+/-1%, 2%, whatever) and pick the shot that has the highest EV of the range. There's just no way a human could compete.

In golf, the problem I was considering more is putting - I agree that there's just no realistic way of consistently shooting a ball 500 yards into a hole with a diameter in the centimeters. I think reading the course becomes alot more important there and without precise measurements the bot is going to have a hard time there. Although maybe the bot would be allowed to probe and measure the area given that humans are allowed to walk around the area, although measuring the speed of a green is already illegal in golf. On the other hand using an opening book is illegal in chess play and we have no problems with computers doing it. On the other hand, maybe just hitting the green on your tee 100% of the time would be enough to bring a bot to the top? Who knows.

they could hammer humans, but we were talking about perfect play here, not just beating humans. They would still be making mistakes and would lose to an improved robot.

You can be sure there is a shot available off the break that pots a red and leaves the balls broken so that a maximum is possible. No human ever attempts to find it, and it would be amazingly difficult for a robot too.

I think perfect play in snooker will be made substantially easier because of what you were mentioning - imperfections in the felt, microfracture in the balls, etc.. It's going to result in a ranging of all results. So it's likely that many possible lines having an EV within 1 point of another so perfection is 'easier' to obtain than otherwise.

All you need to do is break down the board/ball and momentum into whatever desired granularity. The imperfections mean it's likely unnecessary to go to an insane granularity to obtain perfect play. If you really want to go crazy this would be a cool problem to solve with genetic algorithms. A genetic algorithm/GA being basically a sort of monte carlo simulator that is biased by positive results. So you take a random shot, if that shot scored close to perfect then similar characteristics (momentum/location/ball) are more likely to be chosen for the next simulation. Or use the GA to get a very strong play and tweak that via brute force to try to find the perfect play.

There's alot of possibilities to really simplify it down. I'm really confident that perfect play for snooker would not be difficult to obtain. If somebody decides to do this for their masters, I demand credit!

Deep Green, the pool playing robot.

Eh.. checkers? That game is only a few steps in difficulty above tic-tac-toe.

Sure is. When you graduate from tic-tac-toe, give checkers a try.

Negative, The tic-tac-toe and Checkers program is for people with Mongolism only.

So how are you find the program?

Why bother with household robots when you have illegal burmese available? ( my security guard can provide if you are interested )

Checkers is ridiculously hard. If you aren't just some broke-ass internet tough guy, I'll gladly set up a prop match that you don't win 1 game in 50 (against a human, no less).

The real world is a much more interesting place than that.

Why are we bringing in darts and golf etc.

Just consider connect 4. If you go first, you have a forced win, with no need for your opponent to make any mistakes.

Well, their mistake was letting you go first

it would be easy to guess from this that connect 4 boards of different sizes are also won for the first player, or at least drawn. But they aren't! The 6x6, 8x6 and 9x6 games are all a win for the second player (The standard game is 7x6).

The aesthetics of that is marred by the fact that the win is somewhat trivial, I would imagine.

The nine dart finish in darts holds up better. If a player capable of repeatedly making nine dart finishes played first then he would win all those matches even if his opponent played perfectly as well.