In the above 2 links, it's mentioned that if we toss a fair coin ten times then the exact probability that NO consecutive heads come up in succession (i.e. n = 10 and k = 2) is

p(10,2) = 0.14...

So, the probability of at least one pair of heads, or tails, in 10 tosses is approx 1-0.14 ~0.86

Event A: prob. of next toss is always 0.5 and law of large numbers overules everything else (gamblers fallacy applies)

Event B: prob. of having consecutive heads in cluster of 10 tosses is > 0.86

Considering event B only as our universe, can we somehow create a strategy with this probability to have a positive expectation game, maybe related to Penney Ante concept?

The key is Not about increasing bet size after a win Or loss but rather on the condition that "If a coin was tossed 10 x 10 times,

i.e. Ten events B, there would be at least 8 out of 10 events, a consecutive head appearing within an event"...

.i.e. A 86% prob. single event

The short answer is yes. A coin toss is a 51/49 proposition in favor of which ever side is "up" at the start. (Persi Diaconis, Stanford).Quote:algleThe short answer to your question is NO.

A related article but can't find any examples.

Quote:FleaStiffThe short answer is yes. A coin toss is a 51/49 proposition in favor of which ever side is "up" at the start. (Persi Diaconis, Stanford).

At the 'start', meaning......a PAST result? Hmmm, I thought everything was equal? The AP (cough) crew would say its a 50/50 shot.

Wait, wait, let me guess......unless there is a BIAS with the coin? (ROFL)

Ken :)

Quote:FleaStiffThe short answer is yes. A coin toss is a 51/49 proposition in favor of which ever side is "up" at the start. (Persi Diaconis, Stanford).

If heads was up five times and tails the other five at the start, would that even this out?

Quote:Krazycat

Considering event B only as our universe, can we somehow create a strategy with this probability to have a positive expectation game, maybe related to Penney Ante concept?

Try this game (it's easier). Shake up four coins in your hand and lay them down under your palm in order. Two sides to the bet:

Player A) If there are three of either heads or tails in a row , player B pays $3 to $1

Player B) If there are not three in a row player A pays $1 to $1

Take turns shaking the coins so there is no possibility of cheating.

Which would you rather be? Player A or Player B. Or does it matter?

No. There is a bias on each and every toss toward the side that is "up".Quote:mrjjjAt the 'start', meaning......a PAST result? Hmmm, I thought everything was equal? The AP (cough) crew would say its a 50/50 shot.

Quote:FleaStiffNo. There is a bias on each and every toss toward the side that is "up".

Can you give me the short version reason as to WHY, so I dont have to open links.

You do agree?......it is based on a PAST RESULT, correct? One prior toss is the past, correct?

Past result(s) = Gamblers fallacy? You know where I'm heading with all of this so might as well play along.

Ken

Quote:FleaStiffNo. There is a bias on each and every toss toward the side that is "up".

Like the bias toward banker in baccarat?