I'm not sure not paying is wise. However, I would think in most cases, it would be better to take all the deductions you should have for playing pool and also declare the cash from the money league as income. If you take mileage, table time, food & beverage along with pool cues, chalk, etc., I suspect you will have a decent deduction. If the IRS balks at this, you can always argue then it isn't plausible to treat the prize money as income.
With all that said, contact a real accountant for the correct, professional answer. In general, it isn't a good idea to not declare income on your tax returns. If someone files a W9 on you, that means the IRS has been alerted about this income you got. All it takes is for this to catch the eye of one IRS auditor and you could be in a little bit of trouble.