I recently taught it, as I have often done, to a group of relatively new players, and was puzzled by something I had noticed previously on occasions. I explained that you should line up the croqueted ball to go about 5 yards left of hoop 2, because it will tend to "pull" in and finish in front of the hoop. I explained that the "pull" in this cannon is greater than in a load-and-hold stop-shot from the 1st corner to load hoop 2 and stop in front of hoop 1, as the third ball will check the inside of the croqueted ball while the outside will start moving, thus imparting a clockwise spin to the croqueted ball and causing its path to deviate to the right of where it was lined up.

Then I told them to place the third ball in contact with the croqueted ball so that lines joining the centres of the three balls would form a right-angle, and swing straight at hoop 6, allowing the mallet to follow through. That is, do not use a stop-shot action, but neither should you try to push the mallet through the ball - just carry it through. (This method is used with Dawson International balls and may need to be slightly altered for Barlow balls.)

The results were (as usual) quite satisfactory on the whole, but I noticed that in a few of the cannons the croqueted ball seemed to "pull" outwards instead of inwards, finishing 3-4 yards to the left of hoop 2. I assumed that the players were lining the balls up incorrectly, so I started checking carefully the lining up; but still some of them "pulled" out instead of in. I was concerned because if I tell them the ball will pull in, and instead it goes outwards, they would be justified in thinking, "This fellow doesn't know what he's talking about!"

I asked a group of players to come out with me and conduct some experiments, suggesting possible reasons for the outward "pull". We tried swinging in different directions, using a different type of swing, changing the gap between the striker's ball and the third ball, and several other things, but none of them produced the outward "pull". Finally, in a moment of inspiration, I moved the third ball apart from the croqueted ball about 1 mm. This, of course is illegal because the laws require the balls to be in contact, but it was possible that the balls had fallen apart without the players being aware of it. In any case, my intuition told me that moving the third ball away from the croqueted ball would allow the croqueted ball to pull in more easily, rather than go outwards. The clockwise spin might not happen to the same extent, but I could not see why there should be any "outward pull". My intuition was apparently wrong. When we left a tiny gap between the two balls, the croqueted ball deviated outwards instead of pulling inwards! Further thought suggests that the croqueted ball rebounds outward from the third ball as in a cut-rush. This may not be the whole (or correct) story, but at least I can now suggest a reason why the ball "pulls" outwards sometimes: "You did not have all the balls touching".

This reminded me that many years ago we were teaching (as I had been taught) that in a cannon you can increase the distance the rushed ball travels by closing the gap between the striker's ball and the third ball. There was a man (now deceased) who had written a computer programme to simulate the way croquet balls behave, and one day he said to me, "What you are teaching is wrong, you know! My computer simulations show that closing the gap will not make the rushed ball go noticeably further."

I did not believe him, and suggested that his computer programme must be incorrect. I played some cannons with varying gaps to demonstrate that when I made the gap smaller, the rushed ball did indeed go further. He watched it all, then asked, "How are you determining your line of swing?" I answered, "Through the middle of the striker's ball and the point where the other two balls touch each other", since that is what I had been taught. He said, "Then when you close the gap, you are swinging in a different direction. You are hitting more into the rushed ball and less into the croqueted ball. That is why the rushed ball is going further; not because you have closed the gap. If you swing in the same direction you will find that closing the gap makes no difference." I tried it, and found that both he and his computer were quite right. It may have been the first time such a discovery about what happens in a croquet stroke had been made on a computer screen rather than on a lawn!

That is why I now teach players to aim at hoop 6 (for a start), rather than through the point where the other two balls touch; and I no longer teach them that closing the gap (in itself) will alter the distance travelled by the rushed ball. After all, if you play a normal rush a difference of a few mm in the gap between the two balls is hardly going to make any noticeable difference.

In the cannon, there is also the point that changing the gap will slightly alter the amount of "cut" in the rush to hoop 1, but in this cannon that also does not account for any noticeable difference in the length of the rush.

In closing, perhaps I should point out that not all players will aim exactly at hoop 6, as it can depend on how they swing the mallet, the weight of the mallet, and the flexibility of the shaft.

Complexitiy of 3 ball shot is pretty high, but instead of using emperical approach of leave a 1" gap or whatever, I've always simplified problem into 2 two ball shots.

For the 1st corner cannon example, place CB on corner spot, then place SB as if to play croquet shot to target just left of hoop 2. The placement of the 3rd ball (to-be-roqued-ball == RB) will, in this sort of cannon, be less than 90 degrees and hence movement of CB will have no (or very little) effect on RB. For simplicity, play shot as "drive" - so if line of swing is towards hoop 6, then if it were only a 2 ball croquet shot, SB goes somewhere between hoops 4 & 5.

If it were just the SB & RB, and SB was being struck to that point between 4 & 5, then you can now place RB such that it's in a position for a cut rush to hoop 1 (RB touching CB of course). This always gets the direction right, and for this example, gets the distance right too.

For different distances, don't change from a drive, except in attempting extremes - better to change the swing from say, hoop 6, hence changing the direction AND distance that SB travels, and then move the RB to get the correct cut rush angle.