Its time to put on our mathematical hats! 4D, or 4 Digits, is a popular state run gambling game where fine folks place varying amounts of money to wager the outcome of 4 particular digits (no surprise here).
Today we are going to demonstrate why it is a fool’s errand to purchase one of these infernal tickets (or at the very least, show why you are losing good money for every dollar wagered)
For our case study, we are going to use an example of someone laying down 1 dollar on an Ordinary, Small bet (less computation required).
The baseline mathematical equation involved:
Expected Outcome (gain or loss) = Summation of all expected outcomes
We can think of it as the long term, stable outcome of every dollar that is spent on buying 4D. (Think heads or tails, the long term probability is 50 – 50 if you flip enough times)
So on with business.
Total number of possible outcomes = 10,000 (0000 to 9999)
Chance of winning top prize = 1/10000 (1 chance in 10,000)
Prize money of winning top prize = $3000
Expected value in this case = 1/10,000 X $2000 = $0.30 (30 cents)
We repeat this calculation for the 2nd , 3rd prize which yields us $0.20 and $0.08 respectively.
All the other numerical combinations yield us 0 dollars. (There is no money paid out for non winning numbers)
Hence, in the long run, each $1 spent on buying an Ordinary , Small bet will return a value of … 58 cents. That’s a guaranteed loss of 42% for each bet in the long term (and you thought GST was bad)
Yeah but some people do win, right? We aren’t contesting the fact that people do win, but looking at the bigger picture, majority of the people are actually worse off purchasing 4D. Not surprisingly, lotteries are also known as “a tax on the mathematically challenged”.
Now you know.
PS. Big Bet yields you 65.9 cents on average for every dollar wagered. That’s a 34.1% tax.
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