Here is a fairly straightforward hypothetical question on tactics:

Suppose you have won the toss and could be guaranteed of roqueting with either or both of your first two balls as you hit them into the game. Would you choose to hit if first, or second?

My reason for asking is that is seems that as the roqueting ability of top players improves some of them place more importance on winning the toss and hitting in first, though I think I read that DM has on occasions chosen to hit in second. I am talking about advanced-play games, of course, not handicap games.

Suppose also, for the purpose of the exercise, that you ability to play the other shots (including further roquets) and set up breaks is unchanged - the "magic" wears off after you hit your two balls into play. Perhaps we should also assume that the two players are of equal ability and can accurately assess each other's roqueting percentages.

Does the winner of the toss have an advantage if the opponent plays correctly? Or can the opponent contrive to give himself at least an even chance of obtaining the first break by playing the opening astutely? And is the improvement in roqueting ability as you move upward toward the top level going to make any difference to the answers?

Are there any statistics that would help answer these questions?

The question is straightforward, but the answer is not. It depends on how good the players are otherwise.

Suppose that neither player is good enough to justify attempting a 2 ball break, but both can play 3 ball breaks, and can play a reasonable croquet stroke to set one up. Then on the second turn, R will hit and make a defensive leave, (e.g. balls near corners II and IV) from which K (third turn) may attempt to get going, generally by rolling to hoop 1 from corner IV, but if R's leave is not so good this may be much easier. If the player is such a good shot, then the chances of getting a position from which hoop 1 is runnable is reasonable, so K has a fair chance of picking up a break if he is a strong enough player. If K does not attempt to make a break, then Y is guaranteed to have a good chance of a break or a good leave.

Generally if you can guarantee hitting on turns 2 and 4, that is better than guaranteeing hitting just on turn 3, but if UK is good enough to make a 3rd turn break anyway, the advantage is reversed.

A more practical point: it is more important to be the better shot than it is to win the toss, as far as winning the opening goes, unless both players are good shots. Then winning the toss counts for more. Whether you should go first or second may depend on how good the players are apart from their shooting.

Since the players are rarely equally good shots, and the better shot ought to be changing his tactics to make his advantage count, an analysis based on assuming that both players are equally good shots is not so useful.

Thank you for replying. Your analysis sounds reasonable.

One problem in Australia is that in major national events you will play a number of players about whom you know little or nothing, and even if you have played against them in previous years, a lot can have changed in their game since you last played them.

This means that you will probably have to decide your opening strategy on the assumption that they are roughly the same standard as you are in roqueting, setting up breaks, running hoops, etc.

You have said several times that the players are seldom equal in ability, and that is no doubt true, but rightly or wrongly, I suggest to people I teach that they should develop their tactics and strategy on the assumption that the opponent is roughly their equal.

If you are better at roqueting, hoop-running, rushing, setting up breaks, etc., then you will not need much in the way of sophisticated strategy to win the game; and if your opponent is noticeably better than you are in those things he is likely to beat you whatever strategy you adopt. (Of course, this does not mean you should accept defeat. Against a stronger opponent you should be more willing to take risks, whereas many players incorrectly tend to play more cautiously than they would against a weaker player. However taking additional risks still means you are likely, though less certain, to lose.)

As I say to players, "I cannot show you how to beat a better player. All I can do is show you how to be a better player."

I don't really buy this. There are plenty of people I play once every two or three years, and plenty of times I play people I haven't played before. I can still get a lot of information about how good they are from things like watching their previous game, or part of it, looking at their ranking and recent results, watching them as they hit up, even from talking to other people. For another thing, if I know one day that I have a [critical distance] CD of 8 yards and another day I have a CD of 20 yards (these are perfectly sensible numbers for me), I'm likely to adjust my openings accordingly.

I would advise people to see what their opponent does and then adapt accordingly. This was very successful for me when I was an improver, and I will still change small details of my play depending on my opponent.

You will know (or be able to find out quite easily) their handicap and ranking position. That gives you some information about what you are up against. You may also have seen them play during previous rounds and have access to their results in previous games. All useful information.

If you're willing to do more research, the rankings database is a mine of information (including about yourself, not just a potential opponent!)

Better would be to assume roughly the same as an average player of your standard. If you know you are playing to a certain standard because your breaks are (comparatively) good, but hitting is poor), you should not assume the same of your opponent.