Umpa Lumpa Backstory ~ Flipping Coins for $$$.

10,000 Umpa Lumpas, are flipping coins in a football stadium. (yes, from Willy Wonka fame, I figured they're tireless workers and enjoy mundane tasks. Just roll with it.) They are trying to establish streaks of either heads or tails. A streak of 15 consecutive heads or tails, earns the diminutive ones, the right to go down onto the field to the 15 yard line. Over time, the select few Umpa Lumpas who buck the odds (.0004% chance) are greeted by the greedy, evil, WonkaMeister, who is overseeing the entire operation. The WonkaMeister congratulates them for the impressive feat, but quickly establishes that he wants their streaks extended. He wants the streak extended from 15 to 30, and if they don't extend their streak, they will be placed back with the commoners to keep flipping coins. So they are placed at the 15 yard line, and for each successful flip, they are allowed to move 1 yard closer to the coveted end zone. Upon reaching the end zone, they will be released to Willy Wonka, to live happily ever after, in the Chocolate Factory. :tup:

The WonkaMeister is well versed in probability, bell curve, regression to the mean, theory of runs, gambler's fallacy, martingale system, etc. For instance, he knows that 27 in a row, is the equivalent of winning the MegaMillions lottery. (true fact) Also, in 1913, at a casino in Monte Carlo, black came up a record 28X in succession. He knows that there is a wealth of online information pertaining to streaks of 10, 11, 12, etc., most of it addressed as "well the next coin flip has no memory of the last, they are independent trials". He can't find anything on the extreme odds that his expieriment is revealing. The WonkaMeister is ca$hing in on this streak area between 22-30. He doesn't want to fade the commoners at zero, he wants to begin fading the select few Umpa Lumpas that make it close to the end zone. He believes that if he started betting against the commoners, he'd bust out his bankroll with an unfortunate run. In theory, can the WonkaMeister capitalize on this strategy? Betting that individuals on the insane tip of a bell curve, will experience regression to the mean?

BTW, cutbacks within the operation, forced the WonkaMeister to release 500 Umpa Lumpas to Willy Wonka. Hence the backstory behind the iconic characters you see in the movie. :p


Super Moderator
Could you try to pare this down to your main question? It's not wonderfully clear, and it's hard to pull out the main question here from all the colourful detail, although I appreciate you trying to make it interesting..
Thx CowboyBear, the main question is, with regression to the mean, would it be a profitable venture for someone to begin placing bets against someone else's 22-25 streak mark, than starting at your own ground zero? The vast majority of the public get excited at a streak of 10-15, this is where the seductive 'gamblers fallacy' rears it's ugly head. The mindset is, 'that can't continue, I'll bet against it', and thus, the overall lack of discipline & bankroll management is how Vegas was built. But what about the regression that will take place further down on the extreme tip of the bell curve? There is nothing online about that area. All I can find are websites addressing the 10-15 streak, and the message is clear to beware of fading those streaks within the myriad of 50/50 prop bets, they could go on, and on, and on. I try to define in the story that there is no infinite streak; Monte Carlo. Clear as mud??? Sorry, I tend to ramble, please ask any additional questions, I'd like to debate this.


Ambassador to the humans
I'm still not really clear on what you're asking.

However, if we assume that the coin flips really are always independent with a probability of success of .5 then the probability that somebody who has already flipped a streak of 20 will flip another 6 or more is the same as the probability that somebody that is just starting will flip a streak of 6 or more.

However if we assume that the probability of getting a head is different for each person then things change a little bit.