Count where each pit ends
Before every move, work out where the last seed of each pit would land. A pit ends in your store when its seeds equal the steps to it: 1 seed in the sixth pit, 2 in the fifth, and so on down to 6 in the first (how extra turns work).
Do the same for your opponent’s pits, because their extra turns and your lost captures come from the same arithmetic.
Chain extra turns from the store outward
When two pits both end in your store, play the one nearest the store first. Sowing the fifth pit drops a seed into the sixth, which spoils its count, so empty the sixth before you touch the fifth.
The standard opening is the third pit, whose four seeds end exactly in the store. You move again, and the next move can start from a position your opponent has not had time to affect.
Set up captures and guard against them
A capture needs an empty pit on your side with seeds opposite it and a sowing that ends there (how capturing works). Emptying a pit on purpose is often the first half of the plan.
Check the same thing for your opponent each turn. A big pit of yours facing an empty pit of theirs is a target, so move it, or fill their empty pit, before they can reach it.
Do not feed your opponent
Long sowings carry seeds across to your opponent’s side. A seed there is a seed they can bank or keep, and it can also be the seed that fills an empty pit and spoils your capture.
When two moves bank the same number of seeds, prefer the shorter one.
Plan the ending
The game ends when one side is empty, and the other player keeps what is left on their side (how a game ends). Seeds you hold back therefore count for you, and a lead is safest when your opponent is running out of moves.
In a close game, work out the last few sowings in full. With 48 seeds, 24 each is a draw, so one captured seed can decide the result.
Playing the computer
Normal banks the most seeds it can and checks what you could take straight back, but it looks only one reply ahead. Beat it by building a capture that needs two moves, or a chain of extra turns it does not see coming. Hard searches several moves deep, so against Hard the counting has to be exact.