## Bonoloto makes someone a millionaire in the Canary Islands

**Last night’s Bonoloto draw has made someone in the Canary Islands a new millionaire after there was only one winner of the top prize with a ticket purchased at the ticket office in 49 Calle Pérez Galdós in Las Palmas de Gran Canaria.**

The winning numbers for Tuesday 14^{th} March 2023 were: 12-17-20-23-33-46, and only one person matched all six scooping 1,089,781 euros.

The complementary number was 13, and two tickets have been validated in Zaragoza and Madrid for matching five numbers and the complementary, each receiving 74,979 euros.

The Bonoloto also has a return number, which was 7 last night, meaning anyone who matched that gets their money back or a free go next time!

**7 out of 8 Bonoloto numbers were the same in 48 hours!**

A piece of lottery news caught the attention of many this week because in the space of 48 hours, two Bonoloto draws achieved almost identical results, but what were the odds?

The first of the draws were held on March 9th and the winning numbers were 8, 21, 23, 40, 43, and 47; the complementary number was 26 and the refund was 7. Two days later on March 11th, the sequence of winning numbers was 8, 21, 23, 28, 40, and 47; with identical complementary and refund numbers 26 and 7.

In a Bonoloto draw, six numbered balls are drawn out of 49. The “jackpot” goes to the person who matches these six numbers. In addition, a draw includes a complementary, which is a second chance if someone matches five numbers, and a refund number drawn from a second drum numbered 1 to 10.

According to State Lotteries and Gambling, the probability of matching all six numbers is 13,983,816 to 1, and the chance of matching five numbers and the complementary is 2,330,636 to 1. But this is not the probability we are looking for.

Let's go in stages, ball by ball. The probability that the first ball of a draw is repeated is 6/49. The reason is that we have 49 balls and 6 of them are in the previous combination. If we draw a ball again we will have only five numbers to hit out of 48 balls in the drum, that is, the probability of hitting this time will be 5/48.

If we want to consider the probability of two unrelated events, what we must do is multiply their probabilities. Thus, the probability of repeating two numbers between one draw and another is 6/49 multiplied by 5/48, which is equal to 30/2352 or, simplifying, 5/392. The sequence is repeated five times (both draws had five identical numbers), so we repeat this procedure.

The probability of repeating five numbers in two draws is equal to 720 among 228,826,080, or what is the same, one in 317,814. Here we have to consider two possibilities. One, that we want to estimate the possibility of, strictly speaking, five hits and one miss. To do this we should multiply the result by 43/44, the probability of failure. To simplify (and because the difference is small) we are also going to consider the probability that this last figure could be correct and keep the previous probability.

Now we have to factor in the complementary and refund numbers. The complementary one is drawn from the same drum as the previous figures, in which there are only 43 balls left, so the probability of success is 1/43, which when multiplied by the above probability gives us one in 13,666,002.

To obtain the result we only have to multiply by the probability that the withdrawal will also come out (1/10), to obtain a result of a probability of one in 136,660,020. This is the possibility that two Bonoloto draws repeat (at least) five numbers plus complementary and refund.

However, there is still one detail left, and that is that the result was not repeated immediately but after 48 hours, that is, with another draw involved. This implies that we have two possibilities to repeat our experiment. This time we multiply the previous result by two to obtain an approximation of the real probability of the event. This leaves us with a one in 68,330,010 chance as the final (approximate) result.