>>>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......

You're mixing up separate events (the lotteries) with single events (the cards). These are very different sorts of calculations.