How about a random integer generator, and the player places a bet on certain properties of the integer.
ie: an integer whose value is between 1 and 1000 will be randomly generated, select bet amount and what properties you are betting for.
One example would be the randomly generated number is divisible by two, and I bet 5 fake dollars that this is the case. You could have a payout of 95% if they guess correctly, this way you could say house statistically makes money no matter what, or you could just assume that these suckers are addicts and no matter how much they win, will keep playing until they lose it all.
Number is divisible by 3
number is greater or less than a number the user can choose
for the jackpot, the user can guess which specific number will come up (long shot, but hey, some people play the lottery, right?)
If the number is prime, the user automatically gets paid the value of the prime number, or can choose to tripple their previous bet (ie user bets 50 fake dollars that an even number will be generated, if they win they get a payout of 50 fake dollars, if they lose they lose it all. Instead, 101 comes up, which is prime, so they can either take the 101 fake dollars, or they can tripple their bet where if the next randomly generated number is even, they will get a payout of $150 fake dollars instead of only 50)
The randomly generated number will be congruent to x mod y, where user chooses the x and y, and the payout is based on how likely this is to happen.
Number is the same forwards and backwards (such as 1, 11, 22, ..., 99, 101, 111, 121, ..., 202, ..., 999)
value of the digits in the randomly generated integer add up to a number that the user can choose. (ie player expects digits to add up to 5, the integer is 122, 1+2+2=5, player gets paid)
Prime factorization of the integer has some selectable number of some selectable prime number (such as two threes, so then if 45 is the answer, it's prime factorization is 5*3*3, and the user gets paid out)
Anyway I'm sure there are lots of properties of integers you could use to come up with interesting properties to bet on.