Many players assume that if they are playing at a keno game that like most, pays 3 for 1 on a one spot ticket, that the maximum that they can play without risking tax liability is $499 on a one spot, which when hit would result in a winner of $1,497. Actually this results in a net winner of $998, once the price of the wager is deducted. The true maximum that can be played on a ticket in this scenario is $749.99, which when hit would result in a gross win of $2,249.97, and a net win of $1,499.97! Again, no tax form would be required.

In the case of a two spot, which in most casinos pays 12 for 1, the most that can be safely played is $136.35, which when hit results in a gross win of $1,636.20, and a net win of $1,499.85. If a three spot pays 42 for 1, (the most common odds), the most that can be wagered on it is $36.58, which results in a gross win of $1,536.36, and a net win of $1,499.78.

In general on a straight ticket, solving the simple inequality,

T x W < 1500 + W

where T is the odds for one paid on the ticket, and W is the amount wagered will tell you quickly what the maximum wager should be.

Solving the same problem for a simple way ticket is only slightly more complicated. Suppose we mark three numbers, and circle each one of them individually. We’ll play the one way three and the three way twos, and with the added constraint that all the ways will be the same price. What is the maximum that we can play per way on this ticket given the pay rates above?

If W is the price per way, then

42 x W + 3 x 12 x W < 1500+ 4 x W

Solving this inequality gives us W < 20.2702. So if we play $20.27 per way and we hit solid, we will collect $1,581.06. Once we subtract the cost of the ticket (4 times $20.27, or $81.08), we end up with a net win of $1,499.98, and no need to fill in a tax form!

Suppose that we wanted to play the same way ticket, but instead of wagering the same amount on each way, we want to wager enough on the two spots that a two spot will pay, when hit, an amount equal to the solid three alone. If A is the amount wagered on the three spot, and B is the amount wagered on the two spots, then 42 x A = 12 x B. Therefore B = 3.5 x A. Our formula will look like this:

42 x A + 3 x 12 x 3.5 x A < 1500 + A + 3 x 3.5 x A

Solving for A,

168 x A < 1500 + 11.5 x A

and, A < 9.5846 .

So if we play the three spot for $9.58, we will collect $402.36 on it when hit. If we play the deuces for 3.5 x $9.58, or $33.53 per way, we’ll collect $402.36 on each one when hit solid. So if we hit the whole ticket solid, we’ll collect 4 x $402.36, or $1,609.44 gross. Subtracting the price of the ticket, $110.17 from this gives us a net win of $1,499.27!

Well, that’s it for now, Good Luck! I’ll see you in line!