Someone comes to you and says: 'I bet you £1, that if you give me £2 I will give you £3 in return. Do you accept my offer?' What do you respond to him?
The statement is quite confusing, so simplifying it is a must. So, after some rejigging -
If you give me £2, I may give you £3. The bet is £1 that this will happen
I've substituted "promise" for "may", because it's essentially the same thing, but makes more sense when dealing with probabilities. The case is whether you trust them or not:
You trust them
Well done you, now let's see the consequences:
1. You give them £2
2. They give you £3
3. They win, so you give them £1
That was pointless!
You don't trust them
Erring on the side of caution are we? Let's see what could happen:
1. You give them £2
2. They break their promise, and don't give you £3
The statement did not happen, so they give you £1
Oh dear, you could lose £1 as well
You skew your own chances on purpose
The other alternative is that you don't give them the £2 to start with, although you'd seem pretty stupid to do this
1. You don't give them £2
They don't give you £3, because it's dependant on you giving them £2
You did not induce the conditional statement, so nothing else happens
This seems strange, because you'd think you'd have to give them £1, but you never chanced it. A clear example makes this obvious
I bet you £10 that if Red Rum comes first, Lightning will come second
If the condition (Red Rum comes first) never occurs, the bet has no pay-out
As there is no way you can possibly make money on this, no matter how truthful they are, you should NOT take the bet
Interesting question for sure...kinda like one of those teasers but here's my approach/answer to it:
The person being challenged here, should accept the offer. As he/she could walk away with a £2 profit if that persons agree to deal/bet with the person who is initializing the bet. Because, when you give £2 and the person promises to give you £3 in return, that is not including the initial bet he/she placed with you (the challenger) so we have to account for the £1 bet to be included in the profit (£3 - £2).
Should you take this bet?
Yes. But don't give them anything.
The premise that your bet is founded on is "if you give me £2 I will give you £3 in return". As a logical proposition, this is equivalent to saying that "you give them £2" implies "they will give you £3".
Mathematically speaking, an implication is true whenever either the first proposition is false or the second one is true. (E.g., "If pigs have wings, then I'm a monkey's uncle" is mathematically true because pigs don't have wings, regardless of my personal family connections. There's no way for this statement to be proven false except by producing winged swine.)
So as long as you don't give them any money, then the first clause is false ("you give them £2"), making the entire implication true according to propositional logic. And since that's what you're betting on, you win the bet, and they have to give you £1. So you come out of it £1 richer.