# An edge in Coin Toss system?

1. Nov 16, 2012

### scalpmaster

I came across a post here which is puzzling:
http://quant.stackexchange.com/questions/4442/coin-toss-system

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. Nov 16, 2012

### mathman

What sort of edge do you mean?

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

3. Nov 16, 2012

### scalpmaster

Thanks for the reply.Just wondering if we place a bet for consecutive appearance of T or H only after appearance of HTHT or THTH, would there be an advantage since probability is quite high if we count every cluster of 6 tosses as an event instead of every single toss?

4. Nov 17, 2012

### Norwegian

Then what did you get for (1)?
Is your coin endowed with some sort of memory that makes future outcomes depend on previous ones?

5. Nov 17, 2012

### mathman

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. Nov 17, 2012

### Norwegian

In that case, you may want to reconsider your previous note
as you seem to have inconsistent interpretations of "H or T" and "HH or TT".

7. Nov 17, 2012

### mathman

My calculation of (2): First toss anything. To avoid HH or TT, each subsequent toss must be opposite of previous toss. For 5 tosses in a row the probability is 1/32. Therefore the probability of getting HH or TT = 31/32.

8. Nov 17, 2012

### Norwegian

Sure, but then the probability of getting H or T in (1) must be 100%.

9. Nov 18, 2012

### ImaLooser

If you are betting on independent groups of six then results from a previous group will have no effect on the next group.

10. Nov 18, 2012

### scalpmaster

That is not what (2) meant or whether the coin has memory or not.

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.

Last edited: Nov 18, 2012
11. Nov 18, 2012

### Norwegian

Hi there, would you mind informing us of your proposed betting procedure, an in particular how you arrive at your numbers?

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. Nov 18, 2012

### ImaLooser

Actually martingales have infinite expectation. But it only works if you have infinite money.

13. Nov 18, 2012

### mathman

I believe that he simply mispoke in the statement for (1). P(H) = P(T) = 0.5 is what I assumed he meant.