Challenge Questions

Shawn's answer is good, but I like mine better. Unfortunately I can't give me a GA. Fyz agreed, but cunningly added that 'obvious' might not be obvious to all.

Clearly, I'm the only one here with a head .

If it was a 3-course meal, it might be better to settle up for each course, and then swap who starts.

Very intelligent, Kris.

A and B have 0,5 of chance considered independent series of tosses, as I supposed in my response of yesterday. But B to to start has 0,5 of chance, then:

A+B=1

B=0,5A

In my response of yesterday I made an error of interpretation of the problem and I said both A and B have 50% of chance, what could be the solution of other question.

Sorry.

Best regards,

Arturo

Thanks for the complement, I'm glad the explanation helped. I wouldn't beat yourself up over it - compared to some of my slips it's nothing ! Questions get explained better when people like you and make errors, so it's actually doing everyone a favour.

Sorry, I do not agree.

If I start the tossing, I have 50% of chances of getting heads or not.

If I get head, I pay and the case is finished, and both my friend and I have had 50% of chances.

If I get tail, nobody wins. My friend starts a new tossing and my friend and I have again 50% of chances.

Therefore, my friend and I have 50% of chances of paying. It is irrelevant who starts the tossing.

The CR4 answer is the right statistical solution of a series of inter-related tossing, based on an mental analysis with which I do not agree.

The discrepancy lies on the fact that statistical calculus deals with series of inter-related members, and in the reality we deal, very often, with independent members or cases:

Each tossing, in our case, is isolated in itself, I see.

Statistics is the art of mathematically inter-relate facts that are not inter-related.

I know that it is unpleasant to go counter the official statistics.

Please, arguments, not opinions.

Arturo Pérez Rodríguez

I'm sure there'll be a deluge of rebuttals to this, but let me start it off!

If I get head (0.5 probability) on first toss, I pay and my friend is off the hook. If I get tail, I'm not off the hook, since if my friend gets tail I have to toss again so I have a further chance of paying. Therefore my chance of paying is greater than his.

Cheers.......Codey

Are we to understand that you really believe that the first person to toss has the same chances of paying as his companion?

The mistake in your argument is that you say for the first throw that both you and your friend have 50% chances. Actually, on the first throw you have a 50% chance of paying - but your friend does not yet pay:- if you try to "finish the case" at this point, you will be detained as you try to leave the restaurant.

If you still think your argument is correct, maybe you should try an experiment with a friend, using a small stake of (say) one Euro per throw, and with you being the first to toss for each round. Each start with a pile of say 100 Euros (use your own money), and continue until one of you runs out or decides to pull out. Assuming you can toss the throw more often than once every 10 seconds, your friend should be content to play until you run out, as the theoretical average return rate is about Eu0.1667 per throw (or > Eu100 per hour).
As lessons go, this would be quite cheap.

You seem to want to simplify it to a series of non-related tosses. In the case of a number of tosses with the usual heads I win, tails you win scenario then it is 50-50 and no one has the advantage. That is not the case here as all subsequent throws (or not throws as the case may be) are based on the previous results. So it is NOT a series of non-related tosses but a single series of related tosses and has to be treated as such.

Shawn

Please also see my #17

If I get tail, nobody wins.

The who pays for the meal ?

If you get a tail (50% chance), then your friend has a 50% risk of getting a head on the 50% risk that this occurs.

My friend starts a new tossing and my friend and I have again 50% of chances.

I'm not certain of your meaning, but there are two interpretations;

a) The 'new tossing' means that you have first throw again: Trust me, you will eventually get a head.

b) The 'new tossing' means that your friend has first throw: There's only a 50% chance of that happening. ie his risk is 50% of 50% = 25%

Repeat a) and you will always pay. Repeat b) and your comparative risk are 50:25

Another way of viewing it is to consider a sequence of meals over, say, 1000 days. 500 times, you will pay when you toss the coin. On the other 500, your friend only has half a chance of paying. You've payed for half the meals, and you want to toss to see who pays for the rest ?

That's not a very rigorous explanation, but maybe it helps.