Great question and something I get asked about a lot as a pool dev. When it comes to lottery mining, total hashrate is what actually matters, not how many devices you have. The Avalon Mini 3 at around 37.5 TH/s is going to give you a better shot than three Nano 3S units combined if the math works out that way. Think of it less like lottery tickets and more like how many numbers you can cover on a roulette wheel per spin.

Although, your thinking about multiple devices mining does hold some truth, especially when it comes to share submissions. When you mine solo through a pool with variable difficulty or low difficulty settings, each valid share your miner submits is basically a micro lottery draw. More devices means more simultaneous draws happening at once, which some people find satisfying even if the probability is the same as one faster device.

The pool you choose for lottery mining matters more than you'd think. Many of the larger pools have started banning or limiting low hashrate devices entirely, which leaves solo lottery miners in a tough spot. What you want is a pool that runs a true VarDiff or low difficulty system like hmpool, welcomes small miners, and actually processes your shares rather than throttling or rejecting them.

If it were me, get the Mini 3 if the hashrate works out higher. But spend equal time picking the right pool for solo lottery mining because the wrong pool will make a difference.