Is the question "is there a formula you can use to consistently profit at roulette?" NP complete

This is incorrect.

The mathematical principle is called "limits". Let's say we have a fair (i.e. random) coin. Half the time it comes up heads. Half the time it comes up tails. I can't tell you the result of any one coin flip.

If I flip the coin ten times, there is a chance that every time it will come up heads. It is a small chance (given a fair coin) but it is not a 0% chance. We can calculate the odds pretty simply, the function to calculate the probability that n coin flips are all heads is P(n) = (1/2)^n.

For 10 flips this is .097% (about 1 in 1,000)

For 100 flips it is also not zero. It is about 1 in 1,000,000,000,000,000,000,000,000,000,000. It is very unlikely, but it is still not zero.

Mathematically, it is proper to say that at the limit, as n approaches infinity P approaches 0.

When you are using the word "consistently" you invoke a limit. "Consistent" means that as many times as you play... approaching infinity, you will make money.

So mathematically, I can prove, with absolute certainty, that there is no formula to consistently profit at a roulette wheel where an individual spin has a negative Expected Value. Of course, if there is a positive expected value, you will consistently win money... which is how casinos do actually consistently make money at roulette.

You missed his question, Max.

Would you mind going back and dealing with the question I dealt with in my last response.

Of course you are correct Frank. Each spin of a roulette wheel is independent (not affected by what happened before). Thinking that having a run of one color makes it more likely to get the other color is a common human logical fallacy.

If you have a string of 36 straight reds, the probability of it being black the next time would be slightly less than 50% (because of the chance it will be neither).

By the way, the fact that human intuition makes this mistake is sometimes profitable. If I show a good hand, knowing that people won't expect me to have another good hand right away means that I am more likely to make a big bet for value when it happens.

Poker is a whole different ballgame, Max. It is one of my loves also...but I am not in your class.

I appreciate you answering that other question. My point was that the chances of Red or Black were equal...both slightly less than 50%.

If this young man is off base on something as fundamental as this...I wonder why any of this is being discussed.

Im sorry if you feel im being beligerant or giving you a rough time. Nor am i trying to insult your intelligence or disregard your knowledge and ovbiuos mathematical expertise. I do accept all youve said thus far as accepted fact, but as i say above, PROBABILITY IS NOT FACT, THEREFORE NOT CERTAIN. So in reality calculating a CERTAINTY IS IMPOSSIBLE.
YOU CAN ONLY EVER CALCULATE THE PROBABILITY.
THAT MEANS YOU CANNOT ANSWER THE QUESTION WITH CERTAINTY, ONLY A PROBABLE ANSWER.

It is extremely frustrating to me that i cant just go "THERE SEE" and show you the proof. it is simply too valuabe to me. Especially when everybody on the planet believes what i know to be a FACT to actually be MATHEMATICALLY IMPOSSIBLE.

Let me ask you this, Can you calculate for me all the possible wayS to play to profit in the game if you are going to play forever and change strategy not dependat on the JUST the result but ALSO dependant on how much you will win or lose.?
I dont want the probable answer, I want the, PRECISE, or as you say ABSOLUTE CERTAIN AMOUNT OF WAYS THAT YOU COULD PLAY..

Given the variables, i dont see this as an equation that you can answer with certainty, but if you could show me how then what you are saying would make sense to me..

We keep explaining to you that you are incorrect, you keep ignoring us. Probability is a fact, and because of the important mathematical concept of "limits", certainly is possible. I already gave you a perfectly good example of this with my post on coin flips coming up heads each time... did you read it?

Mathematics works on proofs. Starting with basic principles you can prove that something is mathematically impossible. And yes... mathematically speaking we can define the set of every possible strategy then eliminate them as a group from being profitable.

What you are claiming is one of those things that is, in fact, mathematically impossible.

Yes, you can answer the question with certainty because you asked if you can consistently profit. This is not philosophy or metaphysics, it is very straight math. This is the fundamental point you are confused about. The math is not vague, it is very concrete.


Yes, you can. I'm not willing to spend my time doing it for you but yes, you can calculate any and all strategies. You've also mentioned changing strategies "in the stream." This absolutely doesn't matter. If red has come up ten straight times, the probabilities for success are exactly the same as the first spin. There is no value in changing your strategy based on the prior results, previous wins or losses. The past has no influence on the future.

Yes to the first part of the quote. That is exactly what i mean.

AND YEEEEEEEESSSSSSS!!!!!!!
FINALLY AN ANSWER!!
You clearly state that you can mathematically prove with ABSOLUTE CERTAINTY that there is NO system which you can apply in order to consistantly profit at a roulette wheel.

I dont know how much work is involved in providing that proof, but if possible, could you please do so? Please dont feel obliged too, only if it isnt too much trouble.

However, and please dont feel insulted by this, regardless of how you intend to prove it, i know that i can prove the opposite.

I would like you for a moment to suspend disbelief and tell me what you think it would mean for the world of mathematics IF WE WERE BOTH RIGHT AND COULD BOTH PROVE IT?

This may be verging on the the realms of nonsense talk, but if you would just humor and hypothesise with me further it would really help me in deciding what to do with what I BELIEVE to be true...

Thank you soo much for being patient with me. This is actually my first time in a forum, and i have to say its been thouroughly enjoyable regardless of the niggly frustrations along the way..

My apologies to all those whom i may have upset or offended with my words, and Many thanks to all those who have been involved...

Even you FRANK!!

Sure, it is pretty simple.

1. Each spin of the roulette wheel is independent, the result of one spin doesn't impact any future spins.

2. The effective value of a series of spins is equal to the sum of the effective values of each spin.

3. Adding up any number of negative numbers equals a negative number.

4. As the number of spins approaches infinity, the amount of money you make or lose approaches the total effective value (you make money for positive effective value, you lose money for a negative effective value).

Since to make money consistently you need to approach an infinite number of spins to make money consistently you need to have a positive effective value to consistently make money. Since there is no way to get a positive effective value on a series of spins without a positive effective value on individual spins.

Therefore it is mathematically impossible to consistently make money on a roulette table with negative effective value for each spin.

There is your proof.

Thank you MAX. THAT IS EXACTLY WHAT I NEEDED!
What you wrote, difinitively defines the problem as impossible both in theory, and proved through calculus. I HAVE NO ARGUEMENT AGAINST THIS BEING THE TRUTH. Im fully on board with what you say.
However, i also know with 100% certainty the opposite to be also be true and provable. I AM NOT ASKING YOU TO ACCEPT THIS.... WITHOUT PROOF, I WOULDNT EITHER...
I cant provide that to you without divulging details of how i believe it possible, and so we are at an Agree to Agree and Disagree point...

Now, if you can set aside your beliefs for a moment, and just imagine and hypothesise with me on the following question i will trouble you no further..
So.....
IF THERE WERE A WAY TO PROVE IT POSSIBLE, WHAT WOULD THAT MEAN FOR MATHEMATICS? AND WOULD THERE BE WIDER REPURCUSSIONS?

You are at the point of disagreeing with mathematics? It is interesting that you feel that way.

If there were a way to prove it possible, you would have to disprove some principle of mathematics. I would guess the wider repercussions would depend on which of these principles you were disproving.

Yes Max I am. And its a very sad and lonely place because although i believe myself to be intelligent, i have not studied math further than when i started my business degree and so somebody like yourself who has studied math is quite obviously more knowledgeable on the subject than I am.
I like that you say its "interesting" that i feel that way. the word choice suggests that you are actually engaged with what i say rather than dismissing it off the cuff. Either that, or you think that it is interesting that from your point of view i seem to be so convinced by my own thoughts to have deluded myself to believe that maths is somehow wrong and by definition everybody in the world besides me is also wrong..
What is actually most interesting to me is that essentially, this is a case of:
An Established Theory vs A Proposed New Discovery.
What is provably impossible, shown to be provably possible.
THIS IS WHAT THEY CALL A PARADOX.
And i expect that since it has to do with probability and calculating effective value that those are the principles it will affect. i have no idea what the consequences of that would be and wouldnt know where to begin speculating, but im sure its not something that will be brushed under the carpet..
I expect to be ridiculed. Just like any other pioneer of new discovery, until i can unequivocally show facts that can not be disputed, as new truth and prove my point, no one will believe what i have to say.
But heres the thing, i dont care if you or anyone else wants to believe at this point. Because i know that at some point in the future when the time comes to share the knowledge, those who disbelieved will be forced to reexamine thier beliefs and will then be at the point where i currently am trying to work out how the hell what they will have witnessed is even possible.. Fun Times Ahead for ALL !!!

Unless youd like to continue the discussion further, i think that i have said all i need to say and possibly heard all there is to be heard. Again, Many, many Thanks for engaging with me. I really appreciate it. You have really helped me to get a greater understanding of exactly what it is im dealing with. You are a true gentleman. Im sure we will speak again.

Who knows, maybe one day, me, You and Frank will get together for a game of poker and a night filled with discussion as interesting as this one has been..

Numberman1

No!
Beats me why this thread has dragged on for 4 pages..

One last thing..
Id like to use this discussion as part of the material of the book/paper in which i finally present my findings..

Is there anyone whom would rather i not include their comments in my work?

i obviously plan to use pseudonyms and not expose anyones identity, but i would feel all the more comfortable if i were granted permission to use quotes from the body of our discussion.

Please respond with DONT INCLUDE ME if you would rather i not use quotes from your comments, Otherwise i will take from your silence that there is no objection and continue on accordingly...

Like I said earlier, if there was a winning formula, people would have used it to break the bank of every casino on the planet long before now..