Sleeper vs. Immediate repeat

1) Pigeonhole Principle (PHP): There will be at least one repeat of a dozen in 4 spins (excluding zero(es)), i.e. one pigeonhole will contain two pigeons: 1323 or 121. Each pigeon, in this basic dozens example, is equally-likely yet still possessing some default characteristics based on their relationship to other pigeons and underlying event structures, but advanced PHP can render pigeons NOT equally-likely. All subsequent theorems of the Ramsey flavour are entirely built on PHP in terms of multiple repeats over slightly larger limits (except for Erdos; describes structures relating to uniques instead of repeats):

2) Van der Waerden's Theorem (VdW): In 9 trials in Roulette yielding 2 colours, parities or partitions, there will be one Arithmetic Progression (AP) of 3 integers holding the same value with equal distance, i.e. 1,2,3 (consecutive) or 1,5,9 (non-consecutive). There are 16 possible APs in total. Within 9 spins there could be a single AP - or there could be many - but there has to be at least one as a mathematical certainty.

3) Theorem on Friends and Strangers (Friends'): In a group of 6 lines (acting as people) there will be at least one trio the same (friends) or at least one trio different (strangers). Examples: 211134 = 1 trio same + 1 trio different; 111134 = at least 1 trio same; 113246 = at least 1 trio different.

4) Erdős–Szekeres theorem (Erdos): In 3 unique dozens there will be an increasing sub-sequence or decreasing sub-sequence, i.e. 1,2,3 has an increasing sub-sequence consisting of all three numbers; 1,3,2 has a decreasing sub-sequence of 3,2; 3,1,2 has two decreasing sub-sequences, 3,1 and 3,2; 3,2,1 has three decreasing length-2 sub-sequences, 3,2, 3,1, and 2,1. This shows that some permutations involving unique numbers are rarer than others by virtue of this mathematical law; PHP and Ramsey theorems, in turn, are built upon this as the most fundamental law.

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Sleeper vs. Immediate repeat

Post by falkor2k15 » Fri Sep 08, 2017 9:42 am

Take any straight up number, say, number 24. It could take up to around 500 spins maximum for that number to show!

However, bet that the next number will be the same as last, i.e. if 13 was last number then bet 13. If you lose and it's number 32 then bet number 32. Now, we only have to wait around a maximum of 250 spins to hit our number (position/distance 1) instead of 500!

Edit: I encountered 363 for position 1, so I guess this concept's reputation precedes it.

Reddwarf said
"1. Betting on an unique does not work (=guessing game)
2. Betting on a repeat is not going to work (=guessing game)"

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