Birthday Problem quotes / references

[falkor2k15]

Please quote anymore references you can find - specifically with regards to Roulette!!

"I am seriously looking at the following data point about repeaters. Most of the repeaters happen within the last 18 unique numbers. Defining "most" - only in approximately about more than 3500 repeaters do we have an exception and that is a large number. One side of me says that the odds of certain numbers are different from certain other numbers. Other side says that "huh! how can that be". But however, I truly believe because these repeaters happen within 18 unique numbers, "when" the repeat happened is something that might have the potential to be the method, where the payout is going to be 35:1 but the odds are going to be nearly half or a little more than 1/37. As always the issue is to find a practical working method and I think am struggling there."


"At each spin, bet a single chip on each of the previous 7 distinct outcomes
(numbers) of the game and expect the next outcome to be the same as one of those
numbers with a high probability. As per the conventional pay-off ratios of the
game, in order reach a probability close to 0.5 one has to bet on 19 out of the total
38 numbers on the board, and therefore our strategy gives a player a tremendous

edge over all conventional betting strategies with a much lower risk. Note that by
virtue of the observation made in section 1 in the context of the Birthday paradox,
it also suffices to bet on the 7 distinct outcomes of the previous d consecutive
spins (d > 7) and expect to get win with probability greater than 0.5 in case there
are repetitions of numbers within the last 7 spins."


"If I consider 10 roulette spins at a time, in 72.7% of the cases, at least two of the numbers will be repeats. So, if I play the last 10 numbers, the chance is very good (almost 3 out of 4 cases) that one of the numbers will repeat next! Wow! That would bankrupt every casino on the planet in a few days! If the “strategy” would hold true, the probability would rise to 99.8% that the next spin will repeat a number from the last 20 spins! Virtually, play the last 20 numbers and win every time. The cost is 20 units, the payout is 36 units; therefore that player would make a profit of 16 units in every play!

The cold truth is that the famous and appealing Birthday Paradox merely shows the percentage of sets with duplicate elements in the total elements of an exponential set. That's all. So, unsuspecting roulette enthusiasts do NOT rely on the birthday paradox when playing roulette with real money. If you do, don't ask me for a refund later! Mathematically, it is correct to expect that one of the numbers in the last 26 spins will repeat next with a better than 50-50 chance. It is the median skip calculated by the Fundamental Formula of Gambling. Real-life roulette spins and randomly generated roulette numbers validate this law â€" always.

I did check several roulette tables in Atlantic City, 2004. I did not find a roulette marquee showing unique numbers only. Out of 15 numbers, some were repeats â€" from 3 to 7 repeat numbers. Problem is, the skips between Birthday Paradox situations reached 8 spins sometimes! Probably some players wait for 5 or 6 or so skips and then apply the Birthday Paradox. The average amount of unique numbers to play is 12. Must win in two spins to make a profit."


The last source  also had another page about zero "gaps"/"skips" being close together.

[falkor2k15]

OK so the Birthday Paradox seems to be referring to numbers repeating closer together?
23 23 = position 1 repeated = SUPER REPEAT!
23 14 23 = position 2 repeated
23 14 6 23 = position 3 repeated

There is more chance for position 1 then 2 then 3 and so on.... till mainly 18 uniques back.

I think this is ideal for parachuting too?

I still don't understand how that's related to the Birthday Paradox? How was the Birthday Problem translated to the above roulette example? Association seems a bit far-fetched... Again, who are the people and what represents the birthdays?

[praline]

18 people 37 days

98,49% chance of some match (repeat)

[praline]

link:s://:.rouletteforum.cc/index.php?topic=18407.msg170918#msg170918

Reply number 19

[falkor2k15]

I understand - thank you very much for clarifying!