If you want something with much better odds than playing government run lotteries you can solo mine and try to get lucky on finding a bitcoin block yourself. The expected odds are vastly superior to playing the lottery.
All right, let's make some calculations here to see if that is the case.
Antminer S15 has the hashrate of around 28TH/s.
With the current hashrate, ~ 43,000,000 TH/s, the probabilty of finding a block in 10 minutes:
28 : 43,000,000 = 0.000000651 or ~ 0.000065% (which basically means impossible)
However, the situation is not that hopeless if you want to mine a block in a year.
There are ~ 52560 blocks mined per year, so we should multiply that number by 52560:
0.000000651 x 52560 = 0.03421656 or ~ 3.4%
So, the probability of solomining a block in a year is around 3.4% currently.
Antminer S15- costs ~ $1,000
The energy consumption for Antminer S15 is
1.596 kW x 24h x 365 = 13,980.960 or roughly 14,000 kWh per year.
If the electricity price is $0.10, we have additional $1,400 to the costs.
If succeeded in mining a block you are currently getting 12.5 BTC or $49,000.
So, it breaks down like this:
You are risking $2,400 in order to earn $49,000 with 3.4% chance. (Also keep in mind all that noise and overheating).
If you place $2,400 bet with 3.4% win chance on a dice site with 1% house edge(no way I'm encouraging that though) you are going to win $64,482 in case of luck.
Maybe that's why people rarely solomine, if ever.
Regarding the lottery, there are different odds for different lotteries, but let's take Mega Millions for example.
The odds of winning jackpot ~ 1 : 300,000,000 = 0.000000003
If you buy 1,200 tickets with $2,400
0.000000003 x 1,200 = 0.000004 or 0.0004%
Although your win chance is much smaller than that for finding a block with solomining during one year, don't forget that the prize is much higher in Mega Millions(Next Estimated Jackpot: $40 Million), and also with 1,200 tickets you can win some smaller prizes along the way. So, it's hard to say what is better imo.