An automated computer game that takes players through six rounds of random outcomes to determine the next possible strategy. If a roulette ball spins in the left direction three times in the first three spins, it has a 50% chance to go up to a “4” mark and go down to a “1” mark in the fourth spin, and another 50% chance to go the other way.

If the ball spins in the same direction three times in a row, it still has a 50% chance to go up to a “4” mark but its chance to go any further decreases as it heads away from the first three spins (there is always some uncertainty when the next spin is coming). But a third ball, spinning in the same direction as the first three, has an 85% chance of being up to a “1,” and a 60% chance of being “4” in the fourth spin. That means the probability that the fourth ball has any number other than “4” is just 4% — much too small to be used as a winning strategy. What’s more, a roulette ball would get “up” to four numbers in the fifth spin by chance — just the same as the first and second balls that hit it in the third and fourth bounces, and just as the fourth ball that hit it in the fifth bounce, so the probability that the fifth ball is anything more than a “2” is 10% — so the odds that an extra string to follow up an “3” is “3,” again, is less than 1 in 10 million.

All of this is very useful information, but there’s one more level of detail you may wish to check. The fourth ball in a row doesn’t get a “4” again if it comes near one of the eight possible numbers at the other end of the line, even though it had a 50% chance to move that direction in this frame. Rather, the probability that it will get a “4” again on the following frame is set by another part of the machine.

That means instead of a 50% chance that the sixth ball was a “4,” its probability of getting “4” depends on how quickly a “4” and a “2” go down the chain. A ball spinning in the opposite direction as a “4” now has a 5% chance of spinning in that direction, while it’s just a 0% chance it’ll get to be a “2.”

That means that the odds that you’ll roll

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