>>Hi,
>>
>>>Next toss it's not 1:4 you'll get heads, then for a third 1:16 (1:8 or whatever) - it's still 1:2. By the end of 64 tosses, by that logic, like the old grains of sand on a chessboard conundrum, the chances of getting heads would be practically infinity:1.
>>
>>We're talking about the difference between getting heads on any one throw and getting heads *every time* in a series of throws. Your logic would dictate that there's a 50/50 chance of throwing heads an infinite number of times in succession<g>
>
>No, the argument was about the chances of winning the lottery twice, not "*every time* in a series of " entries.
>
>The chances of getting heads FIVE TIMES, in, say, 10 throws is 1:2
>
>The chances of getting heads TWICE in 10 throws are BETTER than 1:2 (I'd take any bet on that!)

If you mean *at least* twice you'd be right. But your logic is still wrong.

How about a deck of cards. The chances of the top card being, say, a king is 13-1. The chances of the second card being a king is slightly better . But the chances of there being two kings on top is 221-1 (13 * 17).

The lottery argument is the same. Start with the odds of winning twice in succession - that's bascially the original chance squared. Given that the odds are so long even making the calculation after playing a few thousand more times the odds aren't much more in your favour......