Quote:IbeatyouracesDon't waste your time. Some people will never learn.

What concerns me is, if JByrd thinks correct math is "horrifically bad math", what does he think is "good math"? Math that suits his needs?

When over a half a dozen members on this forum say "you're wrong" on a math question, shouldn't that be enough? Does he need Wizard to actually come into this thread and agree with us to change his mind? Would it even change his mind?

Quote:ThatDonGuy

Edit: I just ran one, and got two runs where it took 11.92 billion and 15.19 billion tosses, respectively, to get back to 50%. The first one had a heads/tails difference as high as 170,218, and the second as high as 199,861. At one toss per second, the second one took over 480 years.

There's something to think about:

Let "point A" be the starting point, and "point B" the first point where there are 100,000 more heads than tails since A.

Eventually, you "should" get back to zero from A, but that means that there would be 100,000 more tails than heads since B. Let this be "point C".

Getting back to zero from B means you're back to 100,000 more tails than heads since point C. You end up going back and forth between "100,000 more heads than tails" and "100,000 more tails than heads."

Exactly.

Every simulation you will ever run will have a wave form. The losses will grow and grow, reach an apex (in this case 170,218), and then get smaller and smaller until reaching zero.

This will occur every time you run a simulation. Which means Richard A Epstein (and everyone who agrees with that logic) do REALLY, REALLY, REALLY BAD MATH.

Quote:JyBrd0403Exactly.

Every simulation you will ever run will have a wave form. The losses will grow and grow, reach an apex (in this case 170,218), and then get smaller and smaller until reaching zero.

This will occur every time you run a simulation. Which means Richard A Epstein (and everyone who agrees with that logic) do REALLY, REALLY, REALLY BAD MATH.

Not at all. You and Epstein are explaining two different things - both of which, if you ask me, are true.

Epstein et al. say that the differences "tend" to increase - and in my simulations, they do, for no other reason that, the more tosses you have, the more likely it is for there to be a point where, for some number n, the difference = n. No matter what n you choose, such a point "will" exist, just as the difference "will" return to zero. Nothing bad about that math.

You say that, at some undetermined point in the future, the actual fraction of "wins" will match the expected result. Again, with enough tosses, this "should" always happen as well. The only real problem with this is, this is not 100% "fact" unless you have unlimited time - which, unless you (a) become immortal, and (b) develop some form of spacecraft to escape the inevitable point where Earth cannot support life (e.g. because the sun runs out of fuel to heat it), you don't have.

Quote:ThatDonGuyNot at all. You and Epstein are explaining two different things - both of which, if you ask me, are true.

Epstein et al. say that the differences "tend" to increase - and in my simulations, they do, for no other reason that, the more tosses you have, the more likely it is for there to be a point where, for some number n, the difference = n. No matter what n you choose, such a point "will" exist, just as the difference "will" return to zero. Nothing bad about that math.

You say that, at some undetermined point in the future, the actual fraction of "wins" will match the expected result. Again, with enough tosses, this "should" always happen as well. The only real problem with this is, this is not 100% "fact" unless you have unlimited time - which, unless you (a) become immortal, and (b) develop some form of spacecraft to escape the inevitable point where Earth cannot support life (e.g. because the sun runs out of fuel to heat it), you don't have.

The difference may hit 0, but it will never converge on 0. The heads probability will, however, converge on 50%. Jbyrd seems to think they go hand in hand.

Exactly. Two things are true:Quote:CrystalMathThe difference may hit 0, but it will never converge on 0. The heads probability will, however, converge on 50%. Jbyrd seems to think they go hand in hand.

a) The expected difference between heads and tails increases as the number of trials increases; and

b) For an infinite series of flips, there is a 100% probability that the difference between heads and tails returns to zero at some point after the trials begin.

The mistake is in thinking the above is a paradox.

For the first point:

http://mathworld.wolfram.com/RandomWalk1-Dimensional.html

http://mathworld.wolfram.com/Heads-Minus-TailsDistribution.html

For the second:

http://mathworld.wolfram.com/PolyasRandomWalkConstants.html

Quote:ThatDonGuyNot at all. You and Epstein are explaining two different things - both of which, if you ask me, are true.

Epstein et al. say that the differences "tend" to increase - and in my simulations, they do, for no other reason that, the more tosses you have, the more likely it is for there to be a point where, for some number n, the difference = n. No matter what n you choose, such a point "will" exist, just as the difference "will" return to zero. Nothing bad about that math.

You say that, at some undetermined point in the future, the actual fraction of "wins" will match the expected result. Again, with enough tosses, this "should" always happen as well. The only real problem with this is, this is not 100% "fact" unless you have unlimited time - which, unless you (a) become immortal, and (b) develop some form of spacecraft to escape the inevitable point where Earth cannot support life (e.g. because the sun runs out of fuel to heat it), you don't have.

No, that's what's funny, Epstein and I are both explaining the same thing, the Law of Large Numbers. Strike 1.

Epstein says the differences tend to increase "indefinitely", they don't they tend to form a wave, Every simulation you do unless you are immortal and have endless amounts of time, will have this wave. And, that's on your little simulator that makes 480 years in real life take a couple of hours on your computer. Get it, you can simulate billions of years of tosses and it will NEVER do anything else but form that wave.

And now I'm done dealing with you as well. Don't bother responding, I'm blocking you as well. I have no interest in your bad math either.

Wow, if you block half the people on this site the threads actually aren't so stupid. Whoa.

Quote:someoneYes. You keep getting closer and closer to exactly 50%, but you're not guaranteed to actually hit it. Most people will agree that 49.999999999999999999999999999999999999% is very close to 50%. If you need closer you can keep flipping until you get 1000 9's after the decimal place and you can reach these figures with an imbalance between heads and tails.

If you are still struggling to see this, James Grosjean did a blog http://www.gamblingwithanedge.com/the-denominator-where-due-happens a few years ago the explains it very well.

This is another interesting thing. If you actually do the math 49.99999999999999999999% would get you within .00000000000001 of 50%.

100 million trials * 49.99999999999999% = 49,999,999.9999999999

The math doesn't really even match the reality that you can't have a .99999 win. You can't just keep adding 1000 more 9's because in reality you would either be -1 or would go up to 0. You can't have a .999999 win.

So the math you want to do there doesn't really even apply to this situation. 49.999999% would have to be rounded to 50%, just because you can't have .9999999 wins. So, all those 49.9999999% things, where you want to add another 1000 9's after that, would actually have to be rounded off to 50%. In other words you can't really just keep getting closer to 50%, you would actually have to hit 50%, because there is no .9999999 wins.

Quote:JyBrd0403This is another interesting thing. If you actually do the math 49.99999999999999999999% would get you within .00000000000001 of 50%.

100 million trials * 49.99999999999999% = 49,999,999.9999999999

The math doesn't really even match the reality that you can't have a .99999 win. . . . you would actually have to hit 50%, because there is no .9999999 wins.

JB,

First you made me chuckle when you described my response as "horrifically bad math"

Then you made me laugh out loud when you describe ME's response as "horrifically bad math"

Then I fell about laughing when I read the nonsense espoused in your own previous threads where you described the near certainty of making megabucks with d'Alembert

Finally I despaired when you indicated that probabilities are inherently wrong if they are not integers. No. You cannot have 0.9999999 wins. But you can have a 0.99999999 probability of a win.

I cordially invite you to block me. Indeed block your own internet connection, since you know some of the greatest mathematicians to be ignorant fools and clearly you don't want to see the real source of horrifically bad maths and horrifically bad logic to boot.

Save your energy. Go beat up the casinos with your math prowess.

I think we are ALL agreed, though, that a very large n flips of a coin (to simplify) will

result in a close proximity to 50% each.

Now, can we get to this stage-

Probability of < x% heads in n flips? Anyone know the formula for this?

then we might get to-

Probability of <34% reds in n spins. (we will have to consider that for 1 spin, probability is 48.65%, not 50%)

This will tell us the probability we won't win 1/3 of our bets in n spins, which would be a more practical use

of our knowledge. Can anyone help?