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## The Vegas Notion

Published on Sunday, September 04, 2011 in , ,

It's often joked that lotteries are a tax on people who are bad at math.

Being good at math can't always help you win, but it can help prepare you for that rare moment when that good opportunity comes along.

Probably the single most famous example of this is Edward O. Thorp. Like many others before him, he knew that the odds of blackjack changed as the cards were dealt. However, thanks to the use of computers, he was the first to work out how to take advantage of this fact. In this British documentary (story continues in part 2), here's a brief history about the invention of card counting:

On a somewhat smaller scale, Mohan Srivastava, a geological statistician from Canada, took advantage of the type of math he used at work everyday to find a flaw in a Canadian scratch-off game. The game had a tic-tac-toe theme, and the ticket featured exposed numbers, apparently placed in a random manner, arranged on several tic-tac-toe boards. You would then scratch off the hidden part of the ticket, and if any 3 of the numbers appeared in a winning tic-tac-toe arrangement on the board, that ticket was a winner.

Knowing that computers generated these tickets, and that computers have great difficulty with generating true random numbers, he was able to find the hidden flaw in this game. Due to the \$50,000 limit of the game, he also realized that holding on to this secret himself wouldn't make him rich. He played a few games to verify his theory, and then turned his findings over to the Ontario Lottery Commission, who promptly pulled the game.

Sometimes, all it takes to get an advantage in a gambling game is to see a big enough disparity between the jackpot, the cost of playing, and the odds of winning.

When the city of Paris had to default on its municipal bonds, and offered a lottery as an alternative way for bondholders to at least hope to get their money back, a group of people including no less than Charles Marie de La Condamine and Voltaire realized that the combined cost of the tickets was much less than the jackpot being offered.

To take advantage of this, they put together a syndicate that bought up all the bondholder's tickets each month. This made the bondholders happy, because they were at least recouping the cost of their bonds. It made the syndicate happy, because they were guaranteeing themselves a generous profit each month. After 6 months, the government confronted them caught on and confronted the two about this. However, since what they had done was not a crime, there wasn't much the government could do.

This same principle still works today. An elderly couple in Massachusetts has taken advantage of that state's Cash WinFall game, which occasionally offers large jackpots to what is a relatively small number of players, to clear more than \$1 million in winnings.

This type of principle has been used by many to gain an advantage in gambling games over the years. However, even with it's mathematical basis, even using this approach isn't always a sure thing.

When the Sheffield Owlerton Greyhound Stadium offered a record jackpot of £101,110.39 (roughly US\$164,000) for correctly picking the exact winning order of 6 dogs in each of 6 races, one couple decided to run the numbers. It turned out that buying a ticket for every possible permutation would cost £46,656 (around US\$75,000). Like the others above, the idea that they could guarantee themselves a big profit proved irresistible.

They made the bets, and yet still lost. How do you lose when you've covered every possibility? Two other parties held winning tickets, as well. This meant the jackpot had to be split 3 ways, giving each party £33,703.46 (over US\$54,000), which was a net loss.

Even when the math is on your side, there's still no such thing as a sure thing when it comes to gambling.