The short answer
Two nights is the minimum that feels like a safari. Roughly three game drives. Acceptable if safari is one part of a larger trip and you're tight on time.
Three nights is the sweet spot for most people. Five drives, a relaxed pace, and you stop feeling like you've just arrived.
Four nights and more is for people who came mostly for the safari, or who want to split between two camps.
Why two is a compromise
You arrive mid-afternoon. One evening drive. One full day with two drives. One dawn drive, and you leave. That's three drives, one of them at the hot, quiet time of day. It's a taster. You'll see animals, you'll enjoy it, and you'll wish you'd booked another night. Fine if safari is a box to tick on a bigger trip. Thin if it's the thing you came for.
Why three is the sweet spot
Three nights gives you five drives. You stop rushing. You see the same waterhole in different light. You learn the roads a little. And on the middle day, the one where two nights would have you packing, you're instead back out at dawn because you heard the lions calling near camp. That's the moment people remember, and it's the one two nights denies you.
Why four is luxury, not necessity
Four nights earns itself when safari is the point of your trip, not a segment of it. The ideal split is two camps, one southern and one central, so you see different country without feeling like you spent the whole trip driving. If you're self-driving, four nights also lets you absorb one bad-weather day without losing the whole safari.
The day-rate math
Each night is roughly two game drives, one dawn and one dusk. A private lodge drive is three to four hours; a SANParks self-drive day can be longer. Beyond four nights, the returns diminish unless you're a serious wildlife person. The animals don't get better. Your patience for 5am starts does.
The one not to do
One night. It isn't a safari. It's a transfer with a game drive attached. You'll spend more time getting there and back than you will in the bush.