A positive expected value bet is when the odds offered by a bookmaker are higher than the true probability of the event occurring. For example, if a dog in a greyhound race has a true chance of winning 25% of the time (implied odds of 4.0), but the bookmaker offers odds of 5.0 (4 to 1), then betting on that dog represents a positive expected value. Over time, consistently betting on such opportunities should yield profits as you're getting better value than the actual chance of winning.