Tuesday, December 30, 2014

Are you more likely to win 4D on your birthday, with your birth date?

In the 4D lottery, you select a 4-digit number, from 0000 to 999. If your number is amongst the 23 numbers chosen in a thrice-weekly draw, you win a cash prize.

 Feeling lucky during your birthday? Should you bet with your birth date (e.g. 1501 for 15 Jan)?

Here, I randomly selected 2 days for each of the 12 months, and obtained their historical winning occurrences from the Singapore Pools website. I then checked to see if the birth date was the winning number in all draws within a plus-minus two week window.

In theory, only 7.7% of winning occurrences are expected to fall within the window (4 weeks divided by 52 weeks = 7.7%). If there was birthday luck, the actual proportion would be much higher, perhaps above 10%.

The historical outcome, based on my sample of 24 birth dates, is depicted in the chart below.

Source: Singapore Pools, author's calculations
As shown by the light blue bars, majority of winning occurrences occur outside the 2 weeks preceding and following one's birthday. In my sample, only 8.1% of wins were within the window, close to the theoretical expectation. I guess birthday luck doesn't help with the 4D lottery.

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