Willy Wonka / Umpa Lumpa Backstory

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.

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.

Unless WonkaMeister gets paid better than evens, he cannot capitalize on this strategy.

And if he gets paid better than evens, he does not need a full statium of Umpa Lumpas. One would be enough.

Ya lost me a little in the math, but great / funny backstory. Thanks for that!

Thx!, I aim to please.

As stupid / funny as this story is, it got me thinking....

What if you had a dishonest / smart Oompa Loompa? How often can he jump on the 15YL and not cause a red flag by exceeding the standard deviation?

What if all the Oompa Loompas are dishonest?

First of all the correct spelling is Oompa Loompa, as spelled by TJTB. (They are from Loompland)

Now second, and this is were the math comes in....we need to know the trajectory of the coin flips. So are you talking about the orange-skinned, green haired Oompa Loompas, with a dwarf like shape (short legs, big ass) from 'Willy Wonka and the chocolate factory', or are you talking the dark skinned, dark haired, normal shaped, but miniature Oompa Loompas from 'Charlie and the chocolate factory'? :-)

Definitely the ones from WW & the Chocolate Factory, green hair, big rump.

Seriously, isn't there something to be said for 50/50 prop streaks never exceeding 30??? I mean, the world record for roulette is 28 consecutive black. Don't all you Ivy League wannabees see that it has a finite angle, not infinite?

Quote: DHass22

Seriously, isn't there something to be said for 50/50 prop streaks never exceeding 30???

what do you want to say?

Quote: DHass22

I mean, the world record for roulette is 28 consecutive black.

at 18/37 it only requires 1,125,812,984.71 spins on average (1.1 billion) to see 28 in a row.
the 50/50 mark is about 800 million spins.
It could have easily happened more than one time and no one knew exactly how many spins went by.
Gambling time is different from normal time.

30 in a row requires
4,756,907,339.84 spins on average (4.76 billion)
again, could have already happened and no one knew exactly how many spins. Drunk players, dealer shift change.

hey in 100 years one Craps player hit a 154 roll hand.
about a 1 in 5.6 billion shot.

given time, rare events surprise many
the waiting is the hardest part

One of the oompas will probably end up quitting the factory to sell Baccarat systems.

Quote: 7craps

what do you want to say?

30 in a row requires
4,756,907,339.84 spins on average (4.76 billion)
again, could have already happened and no one knew exactly how many spins. Drunk players, dealer shift change.

Under the parameters within the story. Wouldn't the "WonkaMeister" be playing with house money by the time this astronomical phenomenon occurs? He begins placing bets at 22-25 instead of 0? People taking their 1st step off the plane at McCarron Airport (LV) are starting at zero, hence the funding for the strip. People succumb to the odds and bust out their bankroll. I'm wondering if there's value on the extreme/insane tip of the bell curve. There is soo much online literature and YouTube video addressing a streak of 10, most of it understandibly warns caution to gamblers fallacy, and the martingale. No one is addressing more extreme occurances, and that's what I'm questioning, banking on regression to the mean to capitalize. You're right, as Tom Petty sang, "waiting is the hardest part", but what if you had access to those streaks?

Two years later, and still, no one is answering the question...."what if you had access to those streaks?"

It's been a wonderful ride, playing with house money..... Anyone? Buehler?

Nice mental image of the little ones, but you forgot to stipulate the coins were fair, which most of us should know they never are Depending on the coin, normally biased for the heads on flips and not even close for spinning.

Yes, fair coin.

Would anyone be willing to debate this with me on Skype?

Quote: DHass22

Two years later, and still, no one is answering the question...."what if you had access to those streaks?"

It's been a wonderful ride, playing with house money..... Anyone? Buehler?

The streaks are meaningless. You are still playing at 50/50.

I want 50/50, to let Regression to the Mean work to my advantage. If someone is experiencing a 98-100% rate of success or failure, why not fade them down to 90-92%, then move on to the next person experiencing 98-100%??? These individuals are on the extreme tip of the Bell Curve, why not fade'em for Regression sake?

Quote: DHass22

I want 50/50, to let Regression to the Mean work to my advantage. If someone is experiencing a 98-100% rate of success or failure, why not fade them down to 90-92%, then move on to the next person experiencing 98-100%??? These individuals are on the extreme tip of the Bell Curve, why not fade'em for Regression sake?

Regression to the mean doesn't work like that.

More exactly.

If someone is 30-0 on coin flips (100%), and they go 2-2 for the next four, they 'regress' to 32-2 = 94%. And so on.

Regression to the mean does NOT mean there will be more heads than tails if there's a huge streak of tails. To think so is the gambler's fallacy.

You can fade 'em if you like. It'll still be a 50/50 bet with no advantage to be had.

Quote: thecesspit

Regression to the mean doesn't work like that.

+1

Thank you for the prompt reply. I'm well aware of Gambler's Fallacy, researched it. Much of the information on the net refers to streaks of 10, not extreme streaks like we're talking about. I'm convinced that I will eventually lose my bankroll, but I've made soo many withdrawls, that I'm playing with house money. Just lucky over the years?, or is Regression taking it's course? I'm really not counting on "there will be more heads than tails if there's a huge streak of tails". I'm just executing a Martingale at a much later time than the countless millions who have arrived at McCarron Airport in LV on the top of the bell curve, not the tip, which is where I want to meet them.

Quote: DHass22

Thank you for the prompt reply. I'm well aware of Gambler's Fallacy, researched it. Much of the information on the net refers to streaks of 10, not extreme streaks like we're talking about. I'm convinced that I will eventually lose my bankroll, but I've made soo many withdrawls, that I'm playing with house money. Just lucky over the years?, or is Regression taking it's course? I'm really not counting on "there will be more heads than tails if there's a huge streak of tails". I'm just executing a Martingale at a much later time than the countless millions who have arrived at McCarron Airport in LV on the top of the bell curve, not the tip, which is where I want to meet them.

Doesn't make a difference where you sit on the curve. 30 long streaks are rare, ut they are just 3 x 10 streaks. What happened at tail number 16 that suddenly makes a difference? Or is tails number 21?

IF the coin is fair, the next result is 50/50. If the pay out is evens, there is no edge to be had, no martingale saves you. All those previous flips mean nothing, they tell you nothing, they have no value. They are just a small portion of the long haul you've selected and assumed has meaning.

Otherwise you are assuming past results influence the future, which means all the assumptions about 'random coin flips' are not valid, and a different model needs to be made to assess these Ooompa-Loompas. But with the model you state, 30 tails or 10 tails or 500 tails in row makes no difference to the next coin flip (or the next 6 dozen).

I really appreciate your time & replies. Thought provoking debate. I've just been lucky for a long time. Like I said, I will eventually lose the bankroll. I'm not impressed with streaks of 16 or 21, that's not the time to place a bet, it has to be more extreme. There's something to be said for the Guiness Book of World Records record recording on a roulette wheel is 32 consecutive red in a Monte Carlo casino. Streaks have finite tendancies, not infinite. I understand your logic.

Quote: DHass22

Streaks have finite tendancies, not infinite.

True, but this means nothing unless you can predict the future on the next spin/roll.

Quote: DHass22

I really appreciate your time & replies. Thought provoking debate. I've just been lucky for a long time. Like I said, I will eventually lose the bankroll. I'm not impressed with streaks of 16 or 21, that's not the time to place a bet, it has to be more extreme. There's something to be said for the Guiness Book of World Records record recording on a roulette wheel is 32 consecutive red in a Monte Carlo casino. Streaks have finite tendancies, not infinite. I understand your logic.

Your strategy seems to be:

1. Ask for information
2. Thank the people who give you that information.
3. Ignore the information and insist that you were right all along.

The length of the streak is irrelevant. It doesn't matter if it's 10 or 100 or 1000. To be clear: If I flip 1000 coins and they all come up heads (which will happen once every 2^1000 times) the probability of my NEXT flip coming up heads is 1/2. That's it. Independent trials are independent. Not "independent unless if the streak is really really long, in which case the laws of mathematics will make an exception just for you".

Quote: AxiomOfChoice

Your strategy seems to be:

1. Ask for information
2. Thank the people who give you that information.
3. Ignore the information and insist that you were right all along.

LOL!

Begin polite and stubborn is better than rude and stubborn. I find it refreshing.

Quote:

Your strategy seems to be:

1. Ask for information
2. Thank the people who give you that information.
3. Ignore the information and insist that you were right all along.

Quote: dwheatley

Begin polite and stubborn is better than rude and stubborn. I find it refreshing.

The guy can believe whatever he wants, but skipping steps 1 and 2 would be more efficient and achieve the same goals.

Not stubborn, very open to ideas, that's why I'm asking. Family will continue to eat steak, not bologna, for as long as the system works. There are clearly two types of people with this debate. Those that feel a streak can continue off the grid of a bell curve without stopping, and nothing of any length impresses them. I just choose to believe that regression to the mean is undefeated in it's nature, and will pull all things to the center.

Quote: DHass22

Not stubborn, very open to ideas, that's why I'm asking. Family will continue to eat steak, not bologna, for as long as the system works.

Time to buy some bolonga stock...

Quote:

There are clearly two types of people with this debate. Those that feel a streak can continue off the grid of a bell curve without stopping

Nobody is saying that.

Quote:

I just choose to believe that regression to the mean is undefeated in it's nature, and will pull all things to the center.

You can choose to believe whatever you want, but you don't understand what regression to the mean is. No change in probabilities is required for regression to the mean. This has already been explained to you. You choose it ignore it.

Quote: DHass22

I just choose to believe that regression to the mean is undefeated in it's nature, and will pull all things to the center.

Except you told me you understood what that term means, but are using it incorrectly here, again, and holding a falsehold as a belief.

There is no pull to the centre given the axioms you have used for the model you propose. You have to show which axiom is wrong to come to the conclusions you are making, because otherwise you are making a logical fallacy, which means your other conclusions are either incorrect or not built on sound suppositions.

"Nobody is saying that".

I'm sorry, but by stating a streak could go to a 1,000 flips, you are saying that. World record is 32 for roulette, so you choose to ignore it. Debate within reason, not 1,000.

I've been following this stuff for 9 years, and never seen anything above 26. Therein lies my argument, I don't want to fade someone starting at 1, 10, 16, etc., you will lose. It's what the LV Strip is built upon, bankroll mismanagement, emotion, streaks, and an overall lack of discipline.

Quote: DHass22

Family will continue to eat steak, not bologna, for as long as the system works.

Your family's meals depend on how well you do at the tables? Yikes.

Quote: DHass22

I'm sorry, but by stating a streak could go to a 1,000 flips, you are saying that.

And you're saying that you can predict the future (i.e., the end of a streak), which is actually more ridiculous.

Quote: DHass22

"Nobody is saying that".

I'm sorry, but by stating a streak could go to a 1,000 flips, you are saying that. World record is 32 for roulette, so you choose to ignore it. Debate within reason, not 1,000.

This is all simple probability.

The probability of getting 1000 heads in a row is 1 in 2^1000. Now obviously 2^1000 is a massive number (far higher than the number of times someone will ever actually flip 1000 coins), so, yeah, it will never happen.

A streak of 32 (heads or tails) is 1 in 2^31. Worse than 1 in 2 billion. Bad odds, for sure, but if everyone on earth took a turn spinning a roulette wheel (with no zeros, for convenience sake) until their streak ended, you'd expect to see a few 32-streaks. You could easily break this world record in an hour if everyone on earth participated with their own wheel. The point is that, once they hit that 32-streak, their streak is just as likely to go on to 33 as it is to break. The fact that they are currently in the middle of a 32-streak is irrelevant.

Anyway, I'm sorry that you're not capable of doing high school math (at least, I learned this in high school -- I have no idea what they teach in this country), but there is no debate here. You have educated people trying to teach you something, and you're choosing to ignore them. Which, again, makes me wonder -- why did you ask the question in the first place, if you were just going to tell everyone that they were wrong when they gave you the answer?

Quote: AxiomOfChoice

Which, again, makes me wonder -- why did you ask the question in the first place, if you were just going to tell everyone that they were wrong when they gave you the answer?

+1

What's even more amazing is that he resurrected this thread two times...only to ignore everyone!

Quote: DHass22

I've been following this stuff for 9 years, and never seen anything above 26. Therein lies my argument, I don't want to fade someone starting at 1, 10, 16, etc., you will lose. It's what the LV Strip is built upon, bankroll mismanagement, emotion, streaks, and an overall lack of discipline.

A rare event doesn't mean the next flip is not 50/50. The past events do not matter. Regression to the mean is not due to past events (as shown by example).

The LV strip is built on an in built house edge, and encouraging people to play longer and higher, to maximize the house edge.

Discipline is no answer to turn a game around. All it gives you is the ability to play to your plan, not the casino's. Each bet still carries an edge. Bankroll management and discipline arguments are mirages and windmills that the system sellers and method players tilt at, and pretend they will win. It's misguided at best.

Quote: AxiomOfChoice

Your strategy seems to be:

1. Ask for information
2. Thank the people who give you that information.
3. Ignore the information and insist that you were right all along.

Thanks again everyone, I will proceed with caution; all the way to the bank.

Quote: DHass22

Thanks again everyone, I will proceed with caution; all the way to the bank.

To borrow a phrase (facepalm). Thanks for wasting my time. The invoice is in the post.

Quote: thecesspit

To borrow a phrase (facepalm)

+100 ;)


And to the OP: There will be no need for you to resurrect this dumb thread a THIRD time.