>>>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.

Yeah, agreed. I wouldn't be so keen to bet that I'll defo get just 2 heads.

>
>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).

But if you have several decks of cards, as you draw from each, once, your chance of getting a king, in each deck, is 13-1 each deck.
Similarly your chance of winning the lottery, each draw, is the same.

>
>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......

No. Given that the chance of winning the lottery is the same every time, there's nothing special about the 2nd, or 3rd, or 4th ... nth go.
So your chances of winning the lottery twice on the trot are the same as winning it once, then 1,000 entries from then.