An appraisal fee can cost upwards of $150.00. Before you spend that kind of money, you should learn about your game. It sounds like a Mahjong set. Is the set complete? What are the tiles made of? Just because it looks like ivory does not necessarily mean that it is made of ivory. The tiles may be bone, plastic, Bakelite (an early plastic), or a combination of things. The box is important too. Consider its condition, detail, and embellishments. You can find this information online.
You can see if the tiles are made of ivory by looking very closely or using a magnifying glass. Tiny cross-hatching with irregular lines suggests that the material is ivory. If the lines form a pattern, it is man-made. There are other tests as well. If you heat a needle until it's red hot and touch the tile, true ivory will not scorch while bone or plastic will. However, you may not want to mar the surface of your tiles. Mahjong tiles made of plastic or bone can be valuable too.
Once you inform yourself, if you believe the set is very valuable, then take it to an appraiser. But there is much you can learn on your own.