Purchasing lottery tickets is unlikely ever to be profitable, because when the jackpot increases in size to the point where it might be theoretically worthwhile to buy a ticket, so many people buy a ticket that the rules for having multiple winners come into play, which effectively reduces the jackpot significantly.
It's never a good idea.
I will also note that you can dream of yachts and diamonds just as easily, and as plausibly, by not buying a lottery ticket as by buying one. But it's slightly cheaper not to.
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Lottery income is most definitely taxed, although this likely makes little difference to your point.
In the UK it's tax free, anyway.