Losing Hazard: You score if you hit the other cue ball, which should then hit the red ball and pocket the ball to get three points. Winning Hazard: You pot the red ball to get three points. Then you follow it up with a red ball and so on. If a player is awarded a free ball with all 15 red balls still in play, they can potentially make a break exceeding 147, with the highest possible being a 155 break, achieved by nominating the free ball as an extra red, then potting the black as the additional colour after potting the free-ball red, followed by the 15 reds with blacks, and finally the colours. The sets are combined to one single set of 7 which is later setup with a bunch of 8 black balls. Several incomplete sets of this form of croquet are known to exist, and one complete set is still used for demonstration games in the West of Scotland. Two versions of the game are directly governed by the World Croquet Federation, which organises individual and team World Championships. At every instant in time, prey are being born, and prey are dying, and those two rates are precisely equal in magnitude but opposite in sign.

And again for the sake of simplicity, let’s say it’s a constant environment and there’s no particular time at which organisms reproduce or die (e.g., there’s no "mating season"), so reproduction and mortality are always happening, albeit at per-capita and total rates that may vary over time as prey and predator abundances vary. Purely for the sake of simplicity (because it doesn’t affect my argument at all), let’s say it’s a closed, deterministic, well-mixed system with no population structure or evolution or anything like that, so we can describe the dynamics with just two coupled equations, one for prey dynamics and one for predator dynamics. Or, let’s say the predators and prey exhibit cyclic dynamics. "The prey go up, which causes the predators to go up, which causes the prey to crash, which causes the predators to crash." In lecture, even I’ve been known to slip and fall back on talking this way, and when I do the students’ eyes light up because it "clicks" with them, they feel like they "get" it, they find it natural to think that way. Another way to be declared the victor is to knock the 8 ball off the table.

Another way to score is by hitting the red ball first and then one cue ball for two points. You knock over the first domino, which knocks over the second, which knocks over the third. The patent rights for the manufacture of guncotton were obtained by John Hall & Son in 1846, and industrial manufacture of the explosive began at a purpose-built factory at Marsh Works in Faversham, Kent, what is billiards a year later. This is a case where it’s sooo tempting to think in terms of sequences of events; I know because my undergrad students do it every year. Billiards is all about sequences of causal events. You cannot think about this dynamical system in terms of sequences of causal events. You cannot think about equilibria in terms of sequences of causal events, it’s like trying to think about smells in terms of their colors, or bricks in terms of their love of Mozart. But you’re never going to find something that lets you redescribe predator-prey dynamics in terms of sequences of events, each causing the next.

If you’re playing pool, the game can be played in different ways because of the many pool variants out there. If you’re looking for a pool table, you’re in the right place. For a nine-ball pool, you will have nine balls, while a three-ball pool has three balls. Pool can be played with eight balls, which consist of 15 balls. To win the pool game, you will need to pocket the number 8 ball after you have pocketed all seven balls. For example, if you just pocketed a red ball, the next one should be a coloured ball. Hit the cue ball using the other cue ball and then target the red ball, which should not be pocketed to earn two points. Your cue strikes the cue ball, causing it to roll into another ball, causing that ball to roll into the corner pocket. If a player scratches on an 8 ball shot, but fails to pocket the 8 ball, it is considered a foul. The toy car is pushed into a line of dominoes, the last of which falls onto another toy car, which rolls down a ramp and runs into a ball, which rolls down another ramp… Now, you could try to drill down even further, down to the underlying physiological (or whatever) causes of individual births and deaths, and the underlying mechanisms linking per-capita birth and death probabilities to species’ abundances.