Coding classes in South Yorkshire

The model is deliberately simple. The player pots each ball with the same chance p, every shot independent of the last, and always takes red then black fifteen times before clearing the six colours: 36 pots worth 147 points. The break ends at the first miss. The chance of reaching the tenth pot is p multiplied by itself ten times, so the expected value of a break is the value of each ball times the chance of getting that far, added up. The learner writes it as a short loop, then checks it with 200,000 simulated breaks, which agree.

Two lessons come straight out of the table. First, the average and the typical break are different things. At 90 per cent the expected break is 33.9, but half of all breaks are 24 or less, and nearly half are under 20: a few long breaks pull the average up. At 98 per cent the pattern flips, and the middle break is higher than the average. Second, chances that multiply compound fast. Raising the pot rate from 90 to 95 per cent makes a 147 seven times more likely, because the improvement is applied 36 times over.

Now the reality check. The model says a player potting 95 per cent of the time should make a 147 in about one break in six. Yet WST notes only 14 maximums in 46 years at the Crucible, across many thousands of frames played by the top professionals. The model is not just a little out; it is wrong by a huge margin. That is its most useful result, because it points straight at the assumptions: shots are not equally hard, the black is not always available after a red, the cue ball has to be placed for the next shot, and players choose safety instead of risk. A model that fails loudly teaches more than one that nobody checks.

For a teenager in South Yorkshire, learning to code in 2026 means being able to put any model up against the real world before trusting it. The longer argument is in why teenagers should still learn to code in 2026.