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![[Internet math helps dissect the Playwin online lottery]](10lead.gif)
Ashok Hegde
A friend offers to play a game of die with you. The rules are simple: You choose any one of the six numbers. Each time you roll that number your friend pays you a rupee. If you don't roll that number, you pay your friend a rupee. Will you take him on? You don't have to be John Nash to ask your friend to find another sucker.
Sikkim Super Lotto or Playwin, India's first online lottery, is a similar game. Lured by the prospects of striking it rich for a paltry investment of Rs 10, we are blinded to the odds of it actually happening.
Last evening, I bought a Rs 10 ticket from a local Playwin outlet. I had to choose six numbers between 1 and 49. If all the six numbers I pick match those randomly drawn by Playwin, I stand to be richer by Rs 5 crore (before tax).
I brushed up on my rudimentary grasp of probabilities, with a little help from the Internet, to actually figure out how I could lay my hands on the jackpot.
If I buy a ticket every week for the next 250,000 years, I have exactly one chance of pocketing the big booty! Doesn't the friend's offer now seem a lot more sensible?
What You Are Up Against
- You are in room with nine friends. There are 10 boxes, each has a scrap of paper with one person's name on it. Each of you has to randomly dip into any one box and draw out the scrap of paper. What are the chances that you will come up with your own name? The odds are 10:1. Now imagine a 100 people. Your chances are certainly dimmer now. Next, imagine a full-capacity crowd at Eden Gardens, playing this game. How likely do you think it is that you will draw your name? Getting the picture? Finally, try all of Mumbai playing out this charade, and you get a grip on the kind of odds we are talking about.
- How many heads can you toss in a row? Five? That's possible. Ten? Tough. Fifteen? Highly unlikely. Well, you have a better chance of flipping 23 heads in a row than you have of winning the Lotto jackpot.
- Assume you are 30 and have a lifespan of 75. You will need to buy 5975 tickets every week for the rest of your life to have a fair chance of hitting the jackpot.
- The odds of you drawing a hand of three aces in the first round of a three-card game are 1:5525. How many times have you seen that happen? Would you bet on it?
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So, what are the odds really that you will win the jackpot?
If you want to skip the mathematics, try this Lotto Odds Calculator and head straight for winning tips.
But read on if you are interested in understanding the mathematics behind it.
To calculate the odds, you first need to figure out how many unique combinations of six numbers are possible in a field of 49 numbers. For the first number you pick, you have 49 numbers to choose from. Fortyeight for the second, 47 for the third, 46 for the fourth, 45 for fifth and 44 for your last pick. Multiply these (49x48x47x46x45x44=10,068,347,520).
That's just the first step. Remember 'combinations' you studied in high school math? Apply some of those lessons here. There are a total of 720 combinations in which you can draw your six numbers, depending on what order you draw them (6x5x4x3x2x1=720). Now divide 10,068,347,520 by 720 for the total of unique six-number combinations possible in a set of 49. That's 13983816 (approximately 1.39 crore).
What all this mathematics means is that you if you buy one ticket you have one chance in 1.39 crore possibilities of getting it right.
Playwin has now announced that the jackpot of Rs 5 crore (for the April 11 draw) will be divided among those who get five out of six right in case no one gets all of them bang on.
What are the possibilities of someone getting five of their six picks right?
An easy way to do that is to calculate how many ways your pick of six could include five winning numbers and how many ways it could include one non-winning number. Let's assume your pick is 1,2,3,4,5 and 6. There are exactly six ways in which you can get five of them correct: 12345, 12346, 12356, 12456, 13456, 23456. And since 43 numbers remain after you have picked six, there are 43 ways in which you can get one wrong. Multiply 43x6=258. Divide 13983816 by this number to figure out your odds. That works out to odds of 1:54201 that you will get five numbers correct.
The base prize for a five-number win is Rs 50,000 (which will usually end up being a lot higher depending on the number of people who play the game). This amount in itself is no big deal for odds of 1:54201. For a Rs 10 ticket, a fair prize would have been in the region of Rs 5 lakh. But if you factor in the Rs 5 crore, and assuming that 100 others get five of the winning numbers right (only 37 people got it last time) and share the amount, it leaves you with a prize money of Rs 5 lakh + Rs 50,000. That is a fair bet. Of course, we are assuming here that no one gets all six correct.
WINNING TIPS:There are a number of sites offering strategies to play lotto. Here's someone who has spent a lot of time playing and evolving strategies to improve chances of winning at Lotto.
If you don't think they will work for you, here are two of my own…
Don't put any money in a week that has no prize money carried over. It's not that you have a lesser chance of winning, just that the prize money doesn't justify the odds against you. Instead, save your Rs 10 and buy two tickets at the next draw. This cuts your odds by half for that particular draw and also has bigger prize money at stake. Besides, mathematically, too, the odds are marginally better if you buy several tickets of one draw than if you spread it over several draws.
There's a fallacy among bettors that a sequence of numbers (for example 1, 2, 3, 4, 5, 6) is less likely to occur than a random selection (for example 7, 28, 33, 35, 42, 48). This is simply not true. Both of them have an equal chance of being on the winning ticket. How could you use this information? Simple. Most lottery buyers will not pick a sequence. If you pick a sequence, then there is very little chance that you will have to share your winnings. Which means you rake in a bigger prize.
Many punters will bet on their birthdays. This page explains why you shouldn't do that.
Finally, remember: Lotteries make more money for its operators than those who bet on it. There's an old gambler's saying: The house always wins. So, even if you wish to tempt the fates, don't bet the money you set aside for your electricity bill on the lotto.
The author is, by no stretch of imagination, a mathematician. He just used the Internet to get a fix on the mathematics behind lotteries
The Numbers' Game
It is being touted as India's first online lottery. What 'online' means is that the whole betting process is computerised. You can't, however, play it on the Web.
Playwin, which has bagged the online rights for the Sikkim and Karnataka state lotteries, is promoted by the Essel Group, which owns the Zee
Network. Playwin has set up several retail outlets across the country to sell tickets or picks. It's based on the classic lotto game, where you choose six numbers (without repeating them) from 1 to 49. Each pick costs Rs 10.
Every retail terminal is connected via satellite with Playwin's main server. When you buy a ticket, your numbers are recorded on the main server. The technology comes from International Lottery & Totalizator Systems (ILTS), USA.
The draws are held every week and telecast live on Zee TV. The first draw was held on April 5, 2002 and, according to its Web site, 57,000 players won prize money of Rs 66 lakh. The jackpot (for getting all six numbers right) was Rs 2 crore, and there were no takers for it. This has now been carried over for a total jackpot of Rs 5 crore for the April 11 draw. The draws are validated by Ernst & Young.
According to Playwin, 50 per cent of the money generated via ticket sales goes towards prize money. So, "more people playing means bigger prize money".
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Online Resources:
-- Free Lotto
-- How Lotteries Work
-- The Lotto Assistant
-- Easy Money
- Winning the Lottery: Probability and Coincidence
Also Read:
-- Playwin jackpot odds 1 in 14 million
-- Click, pick and win: Free lotto sites
-- Winning Ways: Cracking online contests
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