Roulette vs Slots

Assumption:  all casino events are random.  That is, each roulette wheel number has an equal chance of winning for each spin.  Similarly, each wheel in the slot machine is independent and random.

Roulette  =  (1/38)(50) + (37/38)(-1) = 134% of each bet returned
•  There are 38 numbers, so you have a 1/38 chance of winning each spin, which pays 50 times your bet.  
•  The remaining numbers, 37/38, result in a loss of your bet.  

Slots  =  (1/81)(50) + (26/81)(2) + (54/81)(-1) = 159% of each bet returned
•  Each wheel has 9 numbers (note there is no zero).  Thus, the probability that any two wheel match is 1/9.  
•  For the big win, which pays 50 times your bet, all three wheels must match: (1/9)(1/9)=(1/81).  
•  For the little win, which pays two times your bet, there are three different ways to match two numbers (AB, BC, AC), so the odds are 3(1/9).  However, one of these instances, the big win, is already accounted for, so the little win odds is 3/9 - 1/81 = 26/81.  
•  The remaining 54 combinations are losers, losing you your bet.  (It is important to note that, unlike real slots, you do not "pay to play".)

Thus, slots give a higher return than roulette.

However, there is more to this story.  Since both games give a return over 100%, you would like to play as much as possible.  Torn City only allows a limited number of gambles, however, via the casino ticket system.  Note that roulette allows you to bet 25 times your level, whereas slots is only 5 times--roulette bets are 5 times larger.  To find out which game is better, we multiply the bet by the return:

Roulette:  5 x 1.34 = 6.7
Slots:  1 x 1.59 = 1.59

Clearly, although the return per bet is lower, roulette is the better game since you can place much larger bets!

If you can not understand this, consider the following:  Investment A gives you a 20% return on your deposit.  Investment B gives you a 15% return.  You can borrow $1000 to invest in A, or $5000 to invest in B.  Clearly, even though A is a "better" investment, B will give you more money since you can make a larger investment.

Conclusion:  A smart player will always play roulette!