Coin toss experiment

Coin Toss Experiment..

Rules...


Prior to a coin being tossed the player makes one of the following decisions:-

1. To bet 0 points i.e. no bet.= (no prediction)

2.To bet 1 point on heads or tails.= (prediction)

3.To bet 2 points on heads or tails.= (prediction)

4. To bet 3 points on heads or tails.= (prediction)

5. To bet 4 points on heads or tails.= (prediction)


The coin is then tossed. Being a fair game, the pay out is "even". Bet 1 point win 1 point or loose 1 point etc. Bet 0 points neither win or loose points but the coin is still tossed.

The same rule is used throughout the experiment to determine a 0, 1, 2 , 3 or 4 points decision prior to each toss.

The game continues until the player has made 3000 "predictions".

The correct ( prediction points) - (incorrect prediction points) is then calculated as the final score of the experiment.

The above rules seem to be fair.


Assume that after 3000 predictions the player is ahead by +224 points.


So a final score of +224 would suggest correct 1612 and 1388 incorrect predictions ( in a points sense)

sqr root 3000 x .5 x.5 = 27.38

1612 - 1500 = 112

112 / 27.38 = 4.09 standard deviations above the mean.

That seems a much higher value than one should ever expect in something that is normally distributed and should exist within about 3 standard distributions in a practical sense all of the time.

I think the rules of the experiment are fair, but perhaps , as the points bet are "variable" then I have an incorrect view of the results of the experiment in a standard deviation sense. And am missing a mathematical fundamental.

My counter point is for example: that bet 2 points win/loose 2 points etc. should take care of this concern. And 3000 predictions is more than sufficient for normal distribution to occur and not allow such a result that is basically derived from the gamblers fallacy with a limited step martingale money management strategy attached.


I am at a loss to quantify a result of +224 points in terms of standard deviation when a variable bet amount is applied. In essence my question is how should one correctly, in terms of standard deviation, describe this result?


Thank you so so much in advance for your advice and comments.


regards

Charlie


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The answer depends heavily on the average bet, and to some extent the distribution of the average bet. If you bet 4 on every decision, then 224/4 = 56 decision spread, which is 1528 - 1472.
28 decisions is only 1 st dev above expectations, which is perfectly reasonable.

Even if the average bet is smaller, if you are using a progression the distribution could include many choices of 4 bets, and the result would still be reasonable.

Quote: charlie123

112 / 27.38 = 4.09 standard deviations above the mean.

That seems a much higher value than one should ever expect

Oh oh
1 in abouts 16,000 is no such a small value, imo

and to (N)EVER expect it...
ever

where did you learn that false stuff

Quote: charlie123

in something that is normally distributed and should exist within about 3 standard distributions in a practical sense all of the time.

all of the time, you says

100% false, it has to be (well MAYbe 99.9% false)

where did you learn this crap?
as craps is not (it is) normally distributed either
not ever outside 3 SDs (or 4)

i want names, places, addresses, urls

thank you for your entertaining 1st post
hope you find lots of opinions here

have fun and be good
Sally

Quote: charlie123

I am at a loss to quantify a result of +224 points in terms of standard deviation when a variable bet amount is applied. In essence my question is how should one correctly, in terms of standard deviation, describe this result?

Normalize to outcomes rather than bet amounts. If you have information on each bet, simply divide the points by the wager and get either -1 or +1 for each outcome. Then your stats will make sense and you'll be well shy of 4 SD.

Edit: wait, did I just do your homework for you?

If I understand you correctly. Then this result is +2.34 standard deviations. In real terms.

+224 / 2 = 112

sqr root 3000 x .25 = 27.38.

average bet size =1.75

64 / 27.38 = + 2.337 standard deviations.

Is that what you mean ?

I wish you had done my homework for me but I am a little too old for school. Oh well

Thanx for your swift reply.

If I understand you correctly. Then this result is +2.34 standard deviations. In real terms.

+224 / 2 = 112

sqr root 3000 x .25 = 27.38.

average bet size =1.75

64 / 27.38 = + 2.337 standard deviations.

Is that what you mean ?

I wish you had done my homework for me but I am a little too old for school. Oh well

Thanx for your swift reply.

Yes, this looks more reasonable. However, a progression that trades many small wins for a few large losses is probably more likely than flat-betting the same average amount to show a small total win like this, so the result is even more likely. The distribution of sample results for 3000 tosses may not be perfectly normal yet, so I'd say nothing suspicious here.

I'm in love, I'm all shook up...

coin toss experiment continued......



the rules of the coin toss experiment seem to be fair..



How to determine the standard deviation of the result has provoked some welcome reply's. Which is great.(all replies are good) and I thank everyone for their input..



The measure of standard deviation is off course important. As it is not enough to just be simply ahead or for that matter behind in a points sense. It is the magnitude of being ahead or behind and this is were standard deviation is useful to me. As it suggests the probability of a given result..



So in this experiment where the bet sizes are variable.. And again thanks to all replies, all are welcome, standard deviation of the results can be calculated by:-





Total points won - total points lost = Net points won. (assuming a positive result of course).





Net points won / Total n bets = Average bet size..





Net points won / Average bet size / 2 / sqr root x .25 x n bets = standard deviation value of the experiment result.





Please agree or feel free to correct my thinking.. I will then post the results of my coin toss experiment in a manner that is generally, acceptable to all, in terms of the standard deviation value.



Thanks in advance I think this is a fun and interesting forum..





Charlie

Quote: charlie123

the rules of the coin toss experiment seem to be fair..

I haven't seen any rules about how the coin will be tossed.

Accordingly, I cannot assume it's a fair toss.

Hi..

Firstly a correction:-

Net points won / Total n bets = Average bet size, whoops !!! should be

Total points bet / Total n bets = Average bet size.

The rules about how the coin is tossed....

Random.org coin flipper site is used to generate the coin toss results. As this site offers true R.N.G numbers rather than P.R.N.G number generation. Such as offered by java or excel programmes etc.

Random .org generated data is widely used within the scientific community when random data is required.

And as I have said in my original post.. The prediction is made "prior" to the coin being tossed. And the rules used to determine the bet size or bet / no bet remain constant throughout the experiment.

Hope this satisfies any concerns about the fairness of the coin. Very valid point tho and thanks for raising it.

Quote: charlie123

The rules about how the coin is tossed....

Random.org coin flipper site is used to generate the coin toss results.

Well, that's certainly fair, but it's not tossing a coin.

Hi,

Not an actual coin but no but mathematically no different. Plus a lot easier on the thumb when tossing many thousands of times .lol.

So do you agree with the calculation of standard deviation?

Quote: charlie123

Not an actual coin but no but mathematically no different. Plus a lot easier on the thumb when tossing many thousands of times

Coins aren't fair. Almost all have a bias. Beyond that, almost all tosses introduce another bias.

As an advantage coin tosser, I was interested in your controls on the coin toss.

I don't use my thumb when tossing coins, unless there's a control in place requiring it. I balance the coin across two fingers (index and middle).


You've picked an unbiased 50/50 randomness source, and you're instead testing people's ability to guess the outcome.

Quote: Dieter

Coins aren't fair. Almost all have a bias. Beyond that, almost all tosses introduce another bias.

There's a lovely bit of footage in there where he's doing a controlled toss.


I hope someone jumps in and double-checks your math. I just find the coin tossing far more interesting.

Why do you call it "coin toss experiment" if you don't use coin tosses ?

What exactly are you interested in ? Given a fair random source you can figure out every property of your results by math. What do you want to achieve here ?

Quote: MangoJ

Why do you call it "coin toss experiment" if you don't use coin tosses ?

What exactly are you interested in ? Given a fair random source you can figure out every property of your results by math. What do you want to achieve here ?

I agree. This entire thread just receded into utter senselessness when the OP revealed that he is using a web-based random number generator to be his so-called "coin flip." So the OP is trying to predict the numbers from a random number generator and testing the RNG for randomness? Huh? This seems to be pointless.

Hi.

Thanks to all for your opinions.

I call it a coin toss experiment as it quite simply is a coin toss experiment in a mathematical sense. Using a R.N.G. to produce the integer's prevents the coin " seeming fair to the untrained eye but in fact unfair due to the slight of hand and great skill of " magician's such as Diaconis" influencing the results. Great clip by the way. And so by using a R.N.G site such as random .org the results of the experiment are shall we say much more rigorous.

Please all remember this is a forum about betting strategies and not a forum about " dealing from the bottom of the deck". Such skills are great when no money is involved but rather less mathematically rigorous than the discussion here. Again this forum is about betting strategies and not about slight of hand. However skill full they maybe.

To gordonm888... I am not testing a R.N.G. for randomness. As random .org has been tested for randomness by the general scientific community in many mathematically rigorous ways. And continues to be done so.


The toss of a "fair coin" can be mathematically described as:-


" A Random Walk in 1 Dimension with Zero Drift"


The toss of a "fair coin" tossed by a magician can be mathematically described as :-


" A Random Walk in 1 Dimension with Drift equal to the ability of the magician to influence the result of each toss".


Hence using an R.N.G. to provide integer's.

Again I am not posting to invite discussion about the manipulation of a "fair coin" in a physical toss. My interest in magic tricks is not that great. But I am posting as my interest in betting strategies is great. Please understand the fundamental difference...

I would indeed welcome and have in fact invited someone to " step in with the math" in regards to my calculation of standard deviation where the bet sizes are variable. I am more than happy to be corrected. Once agreement has been reached on this calculation I will then be more than happy to post my results in light of that correction and so be in a way that is acceptable to all. Both in terms of total points and more importantly the standard deviation value.

This is a happy site please let's keep it that way..