Roulette vs Lottery

I was having a chat with a friend for dinner and was talking about a time when I was hanging out with friends at the casino where we played roulette. She criticised me and told me that roulette is a loser's game. However, I remember she told me that she always purchased around $20 worth of lottery tickets every week. 

She justified herself, saying that that if you walked into a casino and played roulette, you don't win much and the odds are against you in the long run. However, she claimed that lottery games involve small sums spent ($20 per week) with the potential for winning massive amounts that can set you up for life.

Let me start with the qualitative arguments I put up to justify my playing roulette. I believe that in both the lottery and roulette, the odds are against you, but I played roulette not with the expectation of getting financial freedom but with the expectation of just having a good time. I played because I wanted to enjoy myself with friends. There is something very exciting about handing over money to someone and then having the fear, anxiety, and excitement of not knowing how much money you will get back. This is why roulette (or blackjack, baccarat, or any other casino card game) is fun. However, the lottery is a different beast. I used to play the lottery before I calculated the odds. When I played the lottery, I did not do so with the expectation of having fun with friends. I played the lottery because I felt trapped in a boring, low-paid job and saw the lottery as an escape. A lottery ticket in my hands was my way out. It provided me with hope that I could one day become a multimillionaire and with those millions all my problems with disappear. Although this is my experience with the lottery, I find that many people I speak to share the same sort of psychology when it comes to playing the lottery.

Let me move on to the quantitative argument. It is possible to walk into a casino with a small amount of money and walk out a multimillionaire. For example, if you put a $25 chip on one number on a roulette table and win four times in a row, since the payoff is $35 for each $1 you put on, then you will get 25*35^4= $37.5 million. The probability of your number showing up is 1/37 = 2.7 per cent. However, to win four times in a row, the probability of that happening is (1/37)^4 = 1/1874161 = odds of 1874160 to 1.

In other words, you can walk into a casino with $25 and walk out with $37 

million but the odds of that happening are about 1.9 million to 1.

What about the lottery?

Every lottery is different depending on which country you look out and which game you look at. However, let us choose a standard lottery game, such as the standard Tattslotto game provided by Tatts Group Limited. The Tatts Group was kind enough to disclose on their website the odds of winning, the prices of tickets, and as well the payoffs given to winners in the last draw. The payoffs of winning Division 1 (the highest payoff) is about $4.3 million. The odds of this happening are 678755 to one for a standing 12-game ticket. The cost of a 12 game ticket is $7.85 as at May 2011.

How in the world does this compare to roulette? Well, let us assume that in roulette you can have a $7.85 chip and in order to win $4.3 million you will need to win a theoretical 3.71654 times in a row (7.85*35^K = $4.3m and solve for K to get K=3.7), and the odds of this happening are 673430 to one, which is better than the lottery but surprising not so much so.

What about betting limits?

Some argue that most casinos have betting limits that will prevent you from putting more than, say, $1000 on the table at once. But this does not matter. If you put $25 on one number on the roulette table and you get it right, you will win $875, and if you put $875 on one number and win again you will have over $30,000. Suppose you take that $30,000 and bet $1000 thirty times. The odds and payoffs are still the same. The house edge for roulette is a little higher than 5% but let's say it's 5 per cent for this example. Suppose I had $100 and I put it on the roulette table. I am expected to get back $95. However, suppose there was a betting limit of $50. I think divide by $100 into two $50 groups and then bet $50 twice. My payoff from the first bet is $47.50 (5% of $50) and my payoff from the second bet is also $47.50 as it is an identical bet. Therefore after two bets my expected payoff is 47.50*2 = $95, the same as if I had just put $100 on the table. 

Conclusion

What this post should prove is that the lottery and the casino are similar in odds and payoffs. You are expected to lose in both games, and you will lose and win roughly the same amount. The problem is that many people view casinos are dirty places where criminals live whereas lottery tickets are often seen as family-friendly and harmless.

No Difference Between Gambling and Investing

Today is the day of the Melbourne Cup, which means over 100,000 people will flock to Flemington to engage in betting on the outcomes of numerous horse races.

Due to personal reasons I will not engage in any betting during the Melbourne Cup as I believe horse racing is animal cruelty. In my opinion, racing a horse is similar to raping a horse. But that is not the main topic of this blog post.

I remember a long time ago I had a friendly argument with a friend over betting versus investing. I put to him the idea that betting and investing are the same thing. He disagreed and believed that betting is a losers game whereas investing is a winners game.

Most agree that conventional investing involves taking ownership of some company or some asset that will appreciate in value in the future thereby making you a profit.

But if you believe an asset will rise in value, is owning the asset the only way to take advantage of this? Why not bet? What is the difference? Usually betting does not involve taking ownership of the asset that will appreciate. For example, suppose I believe that UK house prices will go up in a month's time. My friend believes that if you think UK house prices will go up in a month's time then the way to win from this is to buy a house in the UK. Very simple. This is the conventional way of investing.

However, why not bet? Using IG Index's house price spread betting platform, you can wager that house prices will rise and make money from it. In fact, there are many arguments in favour of betting rather than investing in this case. By betting, you don't actually own the house and therefore you don't have to pay numerous taxes including stamp duty and land taxes. You avoid all sorts of other costs associated with buying houses such as real estate agent fees, lawyers fees, bank fees, and so forth. However, it is not costless to bet on house price increases. IG Index makes money through bid-ask spreads. But nevertheless, what's the difference? Both methods (investing and betting) involve costs. Both methods involve risk. Both methods involve you assessing the situation, taking a position, and making a bet.

There is no difference between gambling and investing.

But my friend believes otherwise. He says that gambling institutions never lose because if it were likely that house prices will rise then they will change the bid-ask spread so that they take a substantial amount of your winnings. But how is this any different to investing? If it were likely that UK house prices would go up, that would already be factored into prices. The high demand for houses would push up prices thereby increasing the costs of buying houses. This effectively increases the costs of betting that house prices will rise. Because house prices are higher, they are more likely to fall. Try this thought experiment. Imagine you have 100 people. Imagine every single one of those people believed house prices will go up. This means they all buy houses and house prices rise. Can house prices go up further? No, it cannot because there are no more buyers. Everyone who had faith in house prices rises has already purchases houses and there are no more buyers left in the market. There can only be selling, and selling reduces prices. Since there are no more buyers, prices cannot go up anymore.

Image: Waffler

The Problem with Election Betting Market Predictions

The betting markets predict a win for Julia Gillard in the 2010 Australian Federal Election (see Punters Back Gillard Victory). Some people believe that betting markets are very accurate predictors of elections, but I am skeptical.

I know of many people who have put large sums of money on Labor to win. These people are people who do not want Labor to win but bet for them so that their sorrows if Labor wins can be compensated for with cash.

The Labor Party may have certain policies that are unpopular for wealthy people, e.g. the mining tax. Wealthy miners who do not want Labor to win may hedge their bets by betting big for Labor. If Labor wins, they win big money from gambling. If Labor loses, they make big money from mining. This would then skew the betting market so that it predicts a Labor victory.

Real Estate Spread Betting

Now that the FIFA World Cup 2010 is underway, there are many betting ads, e.g. from Sportsbet. In the recent Germany vs Australia game, if you think that Germany will win you can put your money where your mouth is and bet on Germany to win.

Wouldn't it be a great idea if you can do the same thing with Australian house prices? Gambling company should allow punters to bet on whether they think house prices will go up or down.

As it turns out, house price spread betting already exists in the UK, as I have discovered in an article in the Times Online about spread betting: "So, is it possible to make money out of property without the boring necessity of actually buying a house, paying stamp duty or dealing with oleaginous estate agents? The answer is yes: by betting on the movements of the British housing market. Spread betting, as it is known, has proved fabulously lucrative for players such as Simon Smith, 33, who makes rather a good living by sitting in his office in Leeds working out what is going to happen to house prices — and placing his money accordingly."

According to the Times article, many home owners are using house price spread betting to hedge against a fall in house prices. On the other side of the equation, renters can use house price spread betting to hedge agaisnt a rise in house prices, so there is a market both ways.

Further Googling has revealed that you can engage in house price spread betting on UK house prices via IG Index. I am not sure whether this site allows Australians to sign up. I am also unsure about the taxation implications of spread betting.

$50 Million Powerball

In Australia recently there was a Powerball game that included a $50 million jackpot. Powerball is a lottery game. Many people at my work had purchased tickets. The jackpot was the largest in Australian history.

What really surprises me is how many people seem to think lotteries are clean and legitimate yet when they speak about games played in the casino they are heavily against it. For example, my dad buys lottery tickets all the time. He warned me however never to go to Crown Casino because "the odds are against you." He reminded me that in its first year of operation, Crown made $250 million profit.

But lotteries make huge profits as well. My dad was the one who told me that for every dollar spent on lotteries, 50 cents must by law go to the Government, 25 cents to the lottery company, and 25 cents to the jackpot. This means that for every $1 that lottery players spend, they can expect to collectively get back 25 cents. Those percentages do not look good.

Still my dad argues that at the casino because there are bet limits and because you play often and because the prizes are small, it is certain that the casino will win and you will lose. However, with lottery you pay a small amount with the expectation of winning big. It is true that in casinos the odds are against you. Your expected profit must be zero otherwise the casino will go out of business in the long run. However, this must also apply for lottery operators. If the odds weren't against you when you play the lottery, lottery operators would go out of business. It does not matter that the prizes won may be bigger. To keep expected profits positive for the operator, that bigger prize must be compensated for by a lower probability of winning. This may explain why in casinos you see quite a few people making money. One casino operator on a documentary on TV said, "We want to make them win a little so they come back. Then we take all their money." Lotteries however are almost impossible to win. My parents have been playing for decades now. They are not millionaires yet.

One could criticize gamblers by saying that their activities have negative expected payoff. However, many other activities have negative expected payoff e.g. watching a movie or having children. It is important then to see gambling as entertainment. Spending time at the casino can be good for socialization. Lotteries don't seem to offer much opportunity for socialization. Rather, they give people the opportunity to imagine that they would be millionaires. My dad always says, "If I won the lottery, I would..." It seems as if he has his whole life planned out, yet this plan is all contingent upon him winning the lottery.