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The most basic answer for the NZ Saturday Lottery is actually about one in a million.
There are 40 balls in the NZ Lottery and you have to get 6 correct answers, so our one-in-chance is 40 * 39 * 38 * 37 *36 * 35 = 2,763,633,600, or about 1 in 2.7 billion.
However, we don't care in which order the our 6 numbers come up, which increases our chances by 6 * 5 * 4 * 3 * 2 * 1 = 720 chances.
So our actual chance of winning for any combination of 6 balls out of 40 are 2,763,633,600 / 720 = 3,838,380, so about 1 in 3.8 million.
However, you can't buy just one combination of 6 balls, you have to buy at least 4 combinations of 6, which makes the basic chance of winning the Saturday lottery 3,838,380 / 4 = 959,595, or about 1 in 1 million.
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