The easiest way to get from Philly to AC without a car would have to be by train. To go from the Airport to AC, you first take a SEPTA R1 train from the Airport to 30th Street station. This part of the trip takes about 15-20 minutes, costs $5 and runs basically all day.
Next take NJ transit from 30th Street to AC. This trip is about 1.5 hours, costs $7.25 and basically runs about 12 times a day.
Total Trip is about 2 hours but you can't beat $13 each way. The trip from the airport to AC by car is 60-70 minutes so you aren't losing much time in comparision to the cost savings. Once you're in AC you can easily get a taxi from the station to your casino for not much $$$. The train cost is probably less than the cost of gas and tolls.
See
http://www.njtransit.com and
http://www.septa.com for train schedules, etc. NJ Transit trains are generally very clean. SEPTA is not as nice. Both are safe.