## Monday, November 15, 2010

### How Much Do You Need To "Buy" the Grand Lotto 6/55?

Filipinos are a gambling nation so news has really excited them that one of the Philippine Charity Sweepstakes lotteries has reached a jackpot of over a half a billion pesos for a single bet of 20 pesos. It has everyone buying tickets ("who knows?") -- even OFWs abroad who are getting friends and relatives in the Archipelago of Pacquiao to buy them a chance to win.  Of course at these high jackpots, some billionaire tayps may be thinking of ways to "buy" the jackpot by betting on all the possible bets. But how much would be needed and is it really smart to do it?

There are 28,989,675 unique 6 number combinations to be chosen from the numbers 1 to 55. At 20 pesos each you need 579,793,500 pesos to "buy" the Grand Lotto, i.e., to place a bet on each possible 6 number combination. Since no winner was found in the draw today, the next draw could be worth about 580 million pesos. You would win for sure but profit would only be P206,500. Unless someone else wins, in which case you lose a quarter of billion pesos! More if there are two or more winners.

At the heart of this is a very famous mathematical formula for the number of unique Combinations of R things selected from a larger collection of N things:
C(R, N) = N!/(R!(N-R)!)
and
C(6,55)=55!/(6!(49!))=55*54*53*52*51*50*49!/(6*5*4*3*2*1)*49!=28,989,675

It's probably not a good idea to "buy" the Grand Lotto until it's worth about a billion pesos!
[This post was inspired by a Tweet from @Kakanturing (Tony Velasquez)]

juanrepublic said...

Wonderful article! :D

Anonymous said...

And on top of this, the prize will still be deducted with, correct me if I am wrong, 30% tax. So it's really not practicable to place bet on all unique 6 number combination unless the jackpot reaches a billion or even more.. :)

Mart said...

i guess you overlooked that you also get a prize for getting 5 (20,000?)or 4 (2,000) or 3 (20) numbers from the winning combination.

Dean Jorge Bocobo said...

Anon, Mart, The biggest danger is really if another person guesses the winning number!

Ramon said...

You overlook the fact that part of your bet goes to the pot. I think it's 50%. If you buy all the possible combinations, the pot will increase by P290 million. Your profit will then be much more than P200 thousand

Jego said...

Actually, you only need 20 pesos to win 500 million clams. If you dont win, you only lost 20 pesos. Pascal would like those odds. :-D