The law of the third: a true pattern that predicts nothing

Each spin, a given number misses with probability 36/37. Over 37 spins it misses every time with probability (36/37)^37, which is about 36.3%. So about 36% of the 37 numbers, 13 or 14 of them, are expected to be absent from any block of 37 spins. The rest appear, several of them two or three times. That is the law of the third, and it is just the binomial distribution wearing a hat.

Repeaters: since only about 24 numbers will appear in the cycle, bet on the ones that have already shown; they are "the ones in play".

Sleepers: since the absent numbers must eventually appear, bet on the ones that have not shown; they are "due".

Both read a distribution over a finished block of spins as information about the next spin. The next spin has a 1/37 chance for every number, whatever the last 20 did.

Wait for a number to appear twice in the first 15 or 20 spins, then bet it straight-up. Each such bet is a 1-in-37 shot at 35:1, which costs 2.70%. The fact that the number recently repeated does not move either figure. Over 100,000 simulated cycles a repeater strategy returned, within sampling error, minus 2.70% of turnover, exactly like betting any other number at random.

Pick a number that has not appeared in 30 spins and bet it until it does. Same 1/37 per spin, same 2.70%, with the additional problem that "until it does" can be a long time: the chance a given number stays absent for another 37 spins after the first 37 is still 36%. Sleepers do not wake up on a schedule.

Because after the fact it is always there. Any 37 spins you look back on will show about 13 absentees, and it feels as if you could have known. You could have known that some numbers would be absent. You could not have known which, and the bets have to be placed before the spin, not after.

Expectation setting. If you bet a single number, the law of the third tells you that a 37-spin drought is normal and a 74-spin one is not rare. If you bet neighbours or sectors, it tells you that a session will have clusters and gaps in the results by pure chance. Reading the board as a record of variance is sensible. Reading it as a forecast is the oldest mistake at the table, and this law is usually how people arrive at it.