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.