Let's say that your odds of winning the lottery are something like: 1 in 23,000,000 - There seems to be a view that if you buy two tickets that your odds are now 1 in 11,500,000. But here's what bugs me about this.....and leads me to think that reducing odds fractions (2 in 23 million) is nothing more than a lie when it comes to talking about odds.
A random sample of 11,500,000 tickets has a 50% chance of containing one of your two tickets. Independently for each one. Your odds in that random sample of 11.5million tickets may be one of the following:
0 in 11.5mil (25% chance)
1 in 11.5mil (50% chance)
2 in 11.5mil (25% chance)
If you buy 11.5million tickets, your odds reduce to 50%, or 1 in 2 - but there's still a chance that if you pick 2 tickets from the 23 million tickets that one of them isn't yours....
0 in 2 (25% chance)
1 in 2 (50% chance)
2 in 2 (25% chance)
And once you've picked the two tickets - and then pick the winner.....
100%*25% (2 in 2)
+50%*50% (1 in 2)
+0%*25% (0 in 2)
Totals to 50% overall for the drawing, but the majority of that remaining 25% is when the '2' in your 1 in 2 chances don't contain any chance of you winning whatsoever.
Reducing odds from 2 in 23million to 1 in 11.5million seems to me to be a form of self-delusion...