The cat leaps out from behind a corner, grabs your leg and runs off. You were stroking it — and suddenly a bite. This is almost never anger; it is the hunting instinct or a warning you missed.
Hunting hands and feet
A cat is a predator, and play is hunting practice: stalk, chase, grab, bite. If someone played with it using their hands when it was a kitten, it learned that hands are prey. An adult cat that does not get enough play finds prey on its own — your feet under the duvet.
Play every day, two or three times for ten to fifteen minutes, with a wand toy or a toy you can drag along the floor. Let the cat go through the whole hunting cycle: creep up, pounce, catch. At the end, let it catch the toy and get a treat or its dinner — that way play ends in prey, not frustration.
Never play with your hands, and do not let children do it either, even with a tiny kitten. In six months the kitten will be an adult cat with the same habits.
If the cat ambushes your feet, do not run or jerk away — that continues the game. Freeze and distract it by throwing a toy.
Biting while being stroked
The cat came to you, it is purring — and a minute later it bites. Usually it gave warnings: the tip of the tail starts to twitch or lash, the ears turn back or sideways, the skin along the back ripples, the cat stops purring and goes still. That means "enough".
Watch for these signs and stop sooner. Many cats like being stroked on the head and cheeks and dislike it on the belly and at the base of the tail. A belly on display is more often a sign of trust than an invitation.
What not to do
Do not punish it or spray it with water: the cat will start to fear you and will not stop hunting. Do not flick its nose or hold it down.
When it is not play
If the cat hisses, flattens its ears, bites hard without any play behaviour, has suddenly become aggressive or will not let you touch a certain spot, this is often how pain or severe stress shows. Take it to a vet.
If a bite breaks the skin, wash the wound with soap under running water and see a doctor: cat bites often become infected. If the cat is not yours or is not vaccinated against rabies, see a doctor the same day without fail.