​USA TODAY Network via Reuters ConnectThe Free Round ContestBig Cedar Golf is running a contest to give a free foursome at Payne’s Valley. The prize is worth about $1,200. Players must guess how many golf balls landed in the water on the 19th hole over the last year. Entries close on Oct 8. This is a chance to play a top course without paying the high green fee. It feels like a game from childhood where you guessed the number of items in a jar to win a prize.The contest relies on a specific number of balls lost. Big Cedar Golf tallied up the count of balls recovered from the drink on that famous hole. The winner will be the person with the closest guess. MyGolfSpy reported that the course sees a lot of play but the exact water loss is the mystery to solve.How to Make a Smart GuessWinning requires some math and a bit of luck. You cannot just pick a random number. Reports note that between 20,000 and 40,000 rounds are played there each year. That is a wide range, but it sets the baseline. You need to figure out how many of those shots end up in the water.Data from Shot Scope shows that for a 100-yard approach shot, the average chance of hitting the water is 46.2 percent. This number covers golfers from scratch to 25-handicap. The 19th hole can play longer than 100 yards, so you might need to bump that percentage up. If the hole plays longer, more players will miss the green and splash the ball.There is another factor to consider. Some players sneak in a second shot just for fun. One observer guessed that roughly 25 percent of golfers do this. If that is true, it adds between 5,000 and 10,000 extra shots to the total count. Using the 46.2 percent splash rate, that adds 2,310 to 4,620 more balls in the water. These numbers are key to making a smart entry.The Risk of OverthinkingIt is easy to get lost in the numbers. The writer who broke this story used AI to help crunch the data. He set the science aside for his final guess. He admitted that he sometimes hits a second ball on par-3s. He believes the second shots are a major reason why the count might be higher than expected.The writer already submitted his own guess. He picked 19,487 balls. He warned readers not to pick that number unless they want to lose to him. This shows that even experts are making educated guesses. The real count depends on weather, skill levels, and how many people try their luck on the 19th hole.Why This Matters to GolfersPayne’s Valley is one of six bucket-list courses in Missouri. It is a hard place to get on without a big budget. The $1,200 value of the prize makes this a real opportunity. Most people cannot afford to play there often. This contest levels the playing field for anyone who can do a little math.The deadline is tight. You have until Oct 8 to submit your guess. That gives you very little time to run the numbers. Do not wait until the last minute. Check the math on the rounds played and the splash rates. Then make your move. Big Cedar Golf is looking for the