Counting or estimating the number of tags is crucial for large-scale RFID systems. The use of multiple readers was recently proposed to improve the efficiency and effectiveness in reading RFID tags. Due to the long processing time, tag identification based counting schemes are often impractical, especially when tags are attached to moving objects. The existing estimation based schemes, on the other hand, suffer from the multiple-reading problem. To address this issue, we propose the Lottery Frame (LoF) scheme, a replicate-insensitive estimation protocol, that is able to eliminate multiple-readings. We show the high accuracy, short processing time and low overhead of the proposed LoF scheme through analysis and simulations.