Comparing different casino bets

A reader writes: "I read where you recommend playing a single zero rather than a double 0 roulette game because the casino edge is lower. I normally bet $5 to $10 per spin but my local casino only offers $25 minimum single zero games. Should I increase my betting level to take advantage of the better odds?"

In order to answer the reader's question, you need to consider not only the difference in the casino's edge but also the amount bet. It's a fact that the casino's edge is higher on a double 0 wheel than on a single 0 wheel. The casino's edge is 5.26 percent on the double 0 (American) wheel for all roulette bets (except the bet on 0, 00, 1, 2, 3, which is higher). On a single 0 wheel (also known as a European wheel), the lack of one 0 reduces the casino's edge on all bets to 2.63 percent. At first glance making a bet on a single 0 wheel appears to be a better choice than betting on a double 0 wheel because the casino's edge is lower.

However, comparing the casino's edge of one bet to another without considering the amount of the bet is dangerous. What you must do is factor the amount of the bet to calculate your average cost per bet. The latter is simply the amount bet times the casino's edge.

Let's take the example of betting $5 per spin on the double 0 wheel. For our calculations it doesn't matter whether you make one single $5 straight up bet on the inside or outside of the layout or make five different $1 bets on the inside of the layout. The result is the same. If your total bet per spin is $5 and the bet has a casino advantage of 5.26 percent, then your average cost to make that bet is 26 cents ($5 times 5.26 percent). Likewise, if you had a total of $10 bet per spin, your average cost is 52 cents ($10 times 5.26 percent).

What does the "average cost" mean? It's simply a measure of how much money the casino expects to win on every $5 (or $10) bet in roulette over time. Obviously, on any one spin you will either win more than $5 or lose the entire $5, but over time you can expect to lose an amount of money equal to the total amount bet times the casino's edge (i.e., your cost for playing). In the short term, you could be ahead (due to volatility) but if you continue to play roulette on an unbiased wheel, the casino's edge will eventually overtake the short-term volatility. The casinos bank on this fact every day that they are in business.

Let's calculate the average cost for making a $25 bet on a single 0 wheel (casino edge is 2.7 percent). If you do the math, the average cost is 66 cents. This is 40 cents more expensive than making the $5 bet on double 0 wheel and 14 cents more expensive than betting $10 per spin.

The bottom line is that on a per bet basis it will cost you less money over the long haul if you bet $5 (or even $10) per spin on a double 0 wheel compared to betting $25 per spin on the single 0 wheel, even with its lower casino edge. The comparison gets even worse when you consider the number of spins per hour. Normally at a crowded $5 (or $10) minimum bet double 0 table, you will average about 30 spins per hour. On less crowded $25 minimum single 0 tables, you are more likely to average 40 to 50 spins per hour. If we use 45 spins per hour as an average, a player's average hourly cost to play roulette for the $5 bettor on double 0 wheel compared to a $25 per spin bettor on single 0 wheel is:

• $5 per spin times 5.26 percent casino edge times 30 spins per hour equals $7.89 per hour cost
• $25 times 2.7 percent casino edge times 45 spins per hour equals $30.37 per hour cost.

Notice the cost per hour on the single 0 wheel is 2.8 times more than on the double 0 wheel. The reason is the more spins per hour and the higher betting level. These two factors more than compensate for the lower casino edge on the single 0 game. Therefore, when comparing the merits of making one bet to another in a casino don't just compare the casino's edge. Factor in the bet size and the number of decisions per hour to get the true picture what the bet will cost you.