Singapore TOTO

In the Singapore game of TOTO, 6 numbers plus one "additional" number are drawn at random from the numbers 1 to 49. In the Ordinary game, players spend $1 and they choose 6 numbers in the hope of becoming instant millionaires. The previous Singapore TOTO’s top prize was 12 million dollars!! Some of you might have had the following thoughts, “What’s the chance of winning the top prize?” “Isn’t it 50%? Win or don’t win!” Apparently it is more sophisticated than that. A prize pool is established at 54% of sales for a draw. Typically, $2.8 million dollars is "invested" in each game - and games are offered twice per week. This is quite a lot for a country of 5.5 million people right?


TOTO Odds
Now we know that the chance of winning TOTO is 1 in 54. What’s the chance of winning the grand prize?
 
Summary of the Prizes (Singapore Toto)

Grp	Prize Amount	Winning Numbers Matched
1	38% of prize pool (min $1 M)	6 numbers
2	8% of prize pool	5 numbers + additional number
3	5.5% of prize pool	5 numbers
4	3% of prize pool	4 numbers + additional number
5	$50 per winning combination	4 numbers
6	$25 per winning combination	3 numbers + additional number
7	$10 per winning combination	3 numbers

Some simple statistics allow you to know that the chance of winning is: 6/45×5/44×4/43×3/42×2/41×1/40=8,145,060
The chance of you winning the top prize is 1 in 8 million! Considering that the total population in Singapore is 5.47 million as of June 2014 and 17% of Singaporeans are millionaires, maybe… you should save the $1 and the chances you becoming a millionaire are higher. J