Coin Toss Simulator

[altenbach]

---

Edjsch wrote:

So here's the question: Say you are flipping a fair coin and there is currently a streak of 10 heads in a row, would you bet the next toss will be heads or tails?

---

You can flip a coin on that outcome. 😄

[Norbert_B]

Ed,

as written, you must not confuse the chance of an individual, isolated event with a row of dependent results (NOT events!). Chances for the event is always 50%.

But chances for the depending results (HHHHHHHHHH or more "H" in 1024 tosses) are less!

Norbert

[Edjsch]

Guys,

All I was trying to prove in my program is what I said, "Say you are flipping a fair coin and there is currently a streak of 10 heads in a row, would you bet the next toss will be heads or tails?"

Altenbach intimated that it is 50-50 (50%). I agree. But how do we "prove" this to disbelievers? Eg, my (normally) very bright engineer co-worker said he'd bet heavily it would be tails. I'm trying to prove him wrong, but my code comes up with 40%, hence my suspicion that I have a coding error. I told my co-worker that he is confusing the low probability of getting 11 heads in a row (1/2048) with what the NEXT toss will be. But I can't convince him. I guess I just should ignore his stubbornness, and advise him to stay away from casinos!

Ed

[Norbert_B]

---

@Edjsch wrote:

[...]and advise him to stay away from casinos!

Ed

---

Guess that is a good advice for him!

The problem indeed is that he (as most common people) confuses the chance of an independant event with the chance of getting a specific setup of following event results.

Norbert

[altenbach]

How can the coin know and remember what happened in the past and then act on it? You can ask him if he thinks it would make a difference if he makes the 11th toss right away, or wait a minute, hour, day or year? Is there a half-life to the "memory"? What if he goes to a new room and uses a new coin for each toss?

After having 10 in a row, the improbably already happened and there is a 50% chance that it continues.

Part of the misconception stems from the fact that some people think that in order for the average to go back to 0.5, something magical needs to happen and the number ot heads and the number of tails will become closer in the future again. In fact, the two numbers most likely continue to diverge. The only reason the average converges to 0.5 is the fact that the number of tosses increase linearly, while the difference between the outcomes only increase with a fractional power.

Ask him what he thinks is a more probably result in the lotto: A (1,2,3,4,5,6) or B (3, 15, 25, 26, 44, 57)...

[Edjsch]

You guys have it exactly right. So why can't we all make a LabVIEW program to prove this? This is where my Bet check box comes in, but I think even that was coming out to 40%, not 50%, which defies all our logic.

[altenbach]

---

@Edjsch wrote:

... which defies all our logic.

---

Is that the royal "our"? I am sure that there are participants who are perfectly happy with the 39% outcome. 😄

[Edjsch]

Altenbach,

But that flies in the face of your previous 50% prediction, no?

Ed

[crossrulz]

---

@Edjsch wrote:

You guys have it exactly right. So why can't we all make a LabVIEW program to prove this? This is where my Bet check box comes in, but I think even that was coming out to 40%, not 50%, which defies all our logic.

---

I already did.  I have an indicator that shows the probability of getting a tails after a streak of 10 heads.  It came to 50%.

Your 40% (actually 39%) is the chance to get a streak of 10 or more heads in 1024 rolls.  This was calculated using Chi-Squared statistics and proven with code.  The probability of getting a heads once a streak of 10 have happened is still 50%

[Edjsch]

Crossrulz,

Thanks. I guess I need to look at your code again. However, my gut still tells me that the probability of getting a streak of 10 or more heads in 1024 rolls is 50%. I just don't see it, even after all your explanation. I guess I need to read up on Chi-squared theory.

Ed