Meta-puzzle

[Charlie Reams]

Here's a puzzle from today's Times (it's a few pages after the article with me in, incidentally):

Let's play a game. I'll toss a coin. If the first three tosses come up heads, heads, tails, I'll pay you £20. However, if it's tails, heads, heads, then you pay me £10. Should you play?

Well, unless I'm utterly confused, the answer is obviously yes. But our friend at the Times disagrees.

Answer: No. It is three times more likely that tails, heads, heads appears. THere are four possibilities for the opening two tosses: heads, heads; heads, tails; tails, heads; tails, tails. In the case of heads, heads, I can't beat you. You just have to wait for a tail to appear. However, in the other three cases you can't beat me. The first occurrence of heads, heads must be preceded by a tail, giving me the win.

Well clearly this is bollocks and the answer to some quite different question. The meta-puzzle is, assuming the answer is correct, what puzzle was actually intended?

[Michael Wallace]

Edit: Put in a hard to read colour.

Is it not just

"I toss a coin repeatedly until either the sequence HHT comes up, in which case I pay you £20, or the sequence THH comes up, in which case you pay me £10, should you play?"

?

[Charlie Reams]

Yes, I guessed something like that. But the question as posed is quite a long way from that. Some subeditor somewhere is hopefully getting an earful.

[Neil Zussman]

I think I've corrected the puzzle moving/adding as few words as possible. My changes are capitalised. They should do this more often, much more fun than a generic heard-it-before maths problem.
Hopefully you won't see this if you don't want to:

Let's play a game. I'll toss a coin. If the three tosses heads, heads, tails COME UP FIRST, I'll pay you £20. However, if it's tails, heads, heads FIRST, then you pay me £10. Should you play?

No. It is three times more likely that tails, heads, heads appears FIRST. There are four possibilities for the opening two tosses: heads, heads; heads, tails; tails, heads; tails, tails. In the case of heads, heads, I can't beat you. You just have to wait for a tail to appear. However, in the other three cases you can't beat me. The first occurrence of heads, heads must be preceded by a tail, giving me the win.