
#1
Nov1612, 05:49 AM

P: 35

I came across a post here which is puzzling:
http://quant.stackexchange.com/quest...intosssystem 2 events: (1) prob(H or T)of a toss = 0.5. (2) prob(HH or TT) in a cluster of 6 tosses > 0.85. If you are betting on event(2) .i.e.A group of 6 instead of the very next toss Can an edge be actually constructed with some kind of progressive betting system? 



#2
Nov1612, 03:15 PM

Sci Advisor
P: 5,937

Note: I got .96875 (=31/32) for (2). 



#3
Nov1612, 09:22 PM

P: 35





#4
Nov1712, 12:36 AM

P: 144

An edge in Coin Toss system? 



#5
Nov1712, 03:30 PM

Sci Advisor
P: 5,937

Note to Norwegian  for (1) I assumed it was a fair coin, so that the probability of heads = probability of tails = 1/2.
Note to scalpmaster  Norwegians comment is correct. Past events have no effect on the outcomes of future events for coin tossing. 



#6
Nov1712, 03:40 PM

P: 144





#7
Nov1712, 05:28 PM

Sci Advisor
P: 5,937





#8
Nov1712, 05:49 PM

P: 144





#9
Nov1812, 12:53 AM

P: 571





#10
Nov1812, 01:16 AM

P: 35

If you win $1 on 9.6 times and lose $3 every 0.4 times out of 10 groups/counts of 6 tosses (applying martingale if necessary only once on 6th toss), it is a positive expectation game conceptually. However, the assumption was that you can only start betting on the 5th toss(or 4th) which becomes unclear whether the advantage still stands(which is my question). Basically, out of 10 groups of 6 tosses, you will find at least 9 groups with a HH or TT in it. However, this HH or TT can occur on the 2nd, 3rd, 4th or 5th toss, and conventional martingale(limited to once) only gives positive expectation from the 4th toss onwards...unless someone can devise another scheme which still gives positive expectation(maybe smaller) but with more coverage. 



#11
Nov1812, 08:22 AM

P: 144

And again, since your coin is fair, and I suppose you are given fair odds on each bet, all bets, both individually and collectively, will have zero EV. That is a fact. Any scheme suggesting otherwise does not work, and that includes your attempt above. If you maintain your claim, you are probably breaking the forum rules, and the strict forum police may strike at any moment. 



#12
Nov1812, 08:38 AM

P: 571





#13
Nov1812, 03:36 PM

Sci Advisor
P: 5,937




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