Math guys??: Mathematics of streaks

Quote: bazooooka

I still contend that there are event sequences where heads will be less than 50%.

Unless it is a biased coin, you are wrong. This is not even worthy of debate. Coins simply don't have a memory. Since the departure of AlanMendelson, you will probably not find anyone to take your side here on that.

If you think you can get 60% right flipping a coin, why don't you prove us all wrong by making millions using the same strategy betting red and black in roulette.

Quote: OnceDear

I think the word you refer to is 'Troll'

I know forum rule one forbids 'All personal insults' and I've seen cases where the accusation 'Troll' has been deemed to be such a personal insult. I don't agree with that implied extension to the rule, but hey, I don't set the rules or their interpretation.

So, Like DD, I will not accuse the OP of being a troll. I will not attack the writer, I will attack the writing:-

Every link, chart, table and bit of narrative that I've seen from the OP has been absurdly wrong and unsupportable. He refuses to desist in posting abject stupidity.

So, I'm going to block the OP, so as to no longer see his posts.

I also block Trolls..

Watch yourself. This comes very close to crossing the line. The OP has at least been polite and seems to be honestly trying to debate this in a civil manner. I think an apology to the OP is in order.

Quote: Wizard

Watch yourself. This comes very close to crossing the line. The OP has at least been polite and seems to be honestly trying to debate this in a civil manner. I think an apology to the OP is in order.

Thanks Mike, I note your rebuke. I also acknowledge that the OP has been polite. I make no observation about his honesty or intent.
I unreservedly apologise for any offence caused to anyone by my post.
The OP remains blocked from my view and now I'm going to also block this thread. In fact, I'm going to self exclude from posting here for a week. Thank you OP.

Quote: bazooooka

It all adds up to around 40% as shown in charts linked below. Flip sequences have different odds than individual flip outcomes.

https://sinews.siam.org/Portals/SiNews2/EasyDNNNews/thumbs/383/117HotHandsTable.JPG

The problem with the chart is, it treats every one of the 14 sets of four flips (besides TTTH and TTTT) equally in terms of counting HHs versus HTs.

Look at the first two columns of numbers - this tells you all you need to know; of the 24 situations where there is an H in one the first 3 positions, 12 of them have that H followed by another H, and 12 have the same H followed by a T.

There are two separate cases that most people, including all the math geeks on this site, seem to be confused about or to lose track of.

1. You encounter a system that you are certain is random. For this case, the previous outcomes have no predictive power over what will happen in the future.

2. Real-life systems. If one observes 100 consecutive coin flips that all come up heads, then one should feel fairly confident that the 101st coin flip will be heads as well - because what one has probably discovered is that the coin flip is not random. Maybe the coin is weighted, maybe there are magnets involved, maybe the person performing the flip has practiced so as to manipulate the coin - all of those explanations are arguably more probable than than the assumption that the coin flip is random but 100 coin flips just happened to have the same result.

All mechanical objects experience "wear" and surface alteration with time and most materials experience inelastic deformation over time. Solid objects are always inhomogeneous to some degree with variations in density throughout the object and small imprecision in dimensions, squareness or roundness/curvature. These things can cause mechanical systems to depart from randomness.

And human operators of gambling systems are capable of insincerity, particularly when they are motivated by self-interest.

So, no matter what the mathematicians say, it is wise for players to keep their eyes open and take note of hot streaks and cold streaks because they may signify the game is not random ( and at worst, that it is rigged.). That's exactly what casino security does - and players should do it too.

Casinos go through extraordinary effort to ensure randomness. Failure to do so would cost them dearly. Humans looking for patterns will nearly always find patterns that don't exist.

Wiz,

Read the link below where a statistics professor explains this to a hedge fund guy who ultimately concedes the point. We're not talking about biased coins. This is a restricted choice issue and more similar to a Monty Hall type problem,

And, yes, there is no way to make money with this unless one were to propose a similar bet (as happened in the below post).

http://andrewgelman.com/2016/02/18/miller-and-sanjurjo-share-5-tips-on-how-to-hit-the-zeitgeist-jackpot/

Quote: Wizard

Unless it is a biased coin, you are wrong. This is not even worthy of debate. Coins simply don't have a memory. Since the departure of AlanMendelson, you will probably not find anyone to take your side here on that.

If you think you can get 60% right flipping a coin, why don't you prove us all wrong by making millions using the same strategy betting red and black in roulette.

I like where you're heading Mike. This is where I was going to go too. Once a conversation reaches this point, it's time for practicality and put up or shut up in my opinion:

bazooooka... I'll bring a fair coin (quarter) that you can inspect to ensure you believe it's fair. We'll toss the coin 10,000 times (or more) and you have to call the heads/tails correctly. You're stating that you can get 60% right... so after 10,000 flips if you're 60% or higher you win. If you've called the flip INCORRECTLY > 40% then you lose. I'd be willing to bet 10's of thousands of dollars. If you truly believe in this paper, and that you have an edge, this should be just free money to you.

What say you? Put up some real money and put this to a REAL test? Otherwise it's quite obvious that this is all just word fluff and we can all move on with our lives.

Quote: bazooooka

Wiz,

Read the link below where a statistics professor explains this to a hedge fund guy who ultimately concedes the point. We're not talking about biased coins. This is a sampling issue and more similar to a Monty Hall type problem,

The Monty Hall paradox is famous, and, like the article you linked to, shows how introducing bias will lead to incorrect conclusions.

Romes,

You can challenge the paper's author yourself . In fact someone else did exactly that. How the bet is structured matters here. This is not about a fair coin or 50/50 expectations.

http://andrewgelman.com/2016/02/18/miller-and-sanjurjo-share-5-tips-on-how-to-hit-the-zeitgeist-jackpot/