NotSureLeh: How much is your 4D lottery ticket worth?

Singaporean loves to gamble, every week you will see people queuing up to buy lottery tickets, hoping that this will be their lucky day. However, have you ever wonder how much is that 4D ticket you purchased worth?

Thanks to math, you can find how exactly how much it is worth.
The table below shows the amount of money you can win when playing 4D using a $1 lottery ticket(depending on whether you can Big or Small):

Monetary value of each prize

Given there is 10000 combination(0000-9999), the odds of striking each prize is as follows:

Odds of striking 4D

Now, given that you know the odds and monetary value of each prizes, you can find the value of your $1 4D ticket by multiplying the respective odds and value of each prize:

From the table above, the 4D ticket is worth 66 cents (Big) and 58 cents(Small) respectively. So what does this mean? 

1. You are spending $1 to buy an item that is only worth $66 cents max. Therefore, if you are a completely rational person, you will not be buying 4D, as you are overpaying for the odds. Another way to look at it will be that you are paying 30-40%+ tax to the government every time you play 4D.
2. If you die die must buy 4D, it is better to buy "Big" as it offer better value as compared to "Small".

So, now that you learn the true value of a lottery ticket, would you still wanna to play?