### Taxes changed everything

Based on the sales of so many gambling books and products, I’m confident there are many more non-professional gamblers out there than professional ones. (By professional gambler, I mean people who get to file their taxes as a “professional gambler”, fitting the narrow definition provided by the IRS.)

In this large pool of non-professional gamblers, some of us are interested in gambling with an edge. That is, we don’t play games where the casino has the edge. We only like to play games where, considering the return of the game itself and adding the casino benefits, we’d get over 100% of our wager back, on average.

But with the new federal tax law (formally known as Tax Cuts and Jobs Act of 2017) in effect for 2018 and later, gambling with an edge has become quite different for non-professionals. It’s now much harder to deduct gambling losses due to the increased standard deduction and a new cap on the amount of state, local, and property taxes that could be deducted. This has changed everything!

(Before we start, let me emphasize that this is not tax advice. It’s merely gambling-related thoughts from a humble non-professional gambler who decided to crunch the numbers and was surprised by the results.)

Let’s say you are living in Southern California. You are married with no children, you have a day job, and you like to take occasional trips to Las Vegas to gamble. You only gamble when you have an edge. You only play the best video poker in town, which according to vpFREE2, is Full Pay Deuces Wild. The highest denomination in Las Vegas is $1.25 a hand, returning 100.76%. Let’s also say you play the game perfectly, with no strategy mistakes. You’d make 0.95¢ a hand. Right?

No! It's probably not a good idea to play this game. You’d lose money.

This is because the federal and state governments would like a share of your win, but want nothing to do with your losses. (After all, they think of gambling as a vice. Why would they want to subsidize it?) In order to understand this, we need to understand your taxes better.

Let's assume you don’t have any income other than your salary and your spouse’s salary, which add up to $130,000 a year. Let's say you file your taxes jointly, and the only income taxes you pay are California state taxes and federal taxes. For the sake of simplicity, I'll also assume you have no adjustments to income, no tax credits, no AMT, etc. Of course your own situation could be very different, but unless you give thousands of dollars to charity each year, have large medical costs, or have already won and lost a lot of money to gambling this year, your situation could be quite similar to the example I'm discussing here. Even if you have those extraordinary deductions, a lot of what I’m discussing below may apply to you, although with a few differences.

Let’s quickly go over your California taxes. Using California's published tax rates, you’d get a personal exemption of $244 and a standard deduction of $9074, making your taxable income $120,682. Your California tax would be $5560, and you’d have a marginal tax rate of 9.3%. (2020 numbers would be very similar, with some slight adjustment for inflation.)

Remember this marginal tax rate. It’s very important for your gambling decisions. It means that for every dollar your income goes up, California wants 9.3¢ of it in taxes.

Your federal taxes are next. The federal tax law has changed a lot for 2018 and later. There are no longer any personal exemptions, but the new federal law gives you a standard deduction of $24,400 for 2019, much larger than previous years.

In our example, it would be better to take the standard deduction, since itemizing won’t save you as much. You’d only be able to deduct your California taxes of $5560 if you itemize. (Even if you pay much more in state and local taxes, the new federal tax law caps the deduction for local taxes at $10,000). According to the IRS's 2019 numbers, your federal taxable income would be $130,000 − $24,400 = $105,600, your federal tax would be $14,949, and you’d have a marginal tax rate of 22%. Once again, remember that 22% number. It means that for every dollar your income goes up, the IRS wants 22¢ of that in taxes.

Now let’s get back to gambling. It’s your first trip to Las Vegas in the year. You sit down at your favorite Full Pay Deuces Wild machine, and you play one hand. What are your real expectations?

If you win some money, you have gambling income, and your taxes go up a little. If you lose some money, you have gambling losses, but your taxes don’t go down! This is because you need to have a large gambling loss before it would be better to itemize deductions instead of taking the standard deduction. The standard deduction is $24,400, and if you itemize, you’d only have $5,560 in state taxes to list as itemized deductions. For the itemized deductions to be a better choice, you’d need to have at least the difference of those two numbers, $18,840, in gambling losses. But even that is not enough. On gambling losses, the IRS says “You CANNOT deduct more than the amount of gambling income you report on your return”. So you’d need to have at least $18,840 in gambling income and $18,840 in gambling losses for the year. You may very well be in such a situation, but it needs a lot of gambling to get there. Still, even if you are in such a situation, a lot of the following discussions may apply, with a few differences.

Let’s look at the actual numbers for your favorite game. I used the Wizard Of Odds Video Poker Strategy Maker to calculate the odds of perfect play for Full Pay Deuces Wild. The total return, ignoring taxes, is 1.007620. So it's a 100.7620% game, where you may expect a 0.7620% edge against the casino.

But the game changes vastly if you incorporate taxes in evaluating the game. The Natural Royal Flush win, previously worth $998.75 (4000 coins of 25¢, minus your original wager of $1.25), is now worth just $686.14, since the state and federal governments want $312.61 of your win. The Four Deuces are similar: they are now worth just $170.89 instead of $248.75. This goes all the way down to the Straight, which would be worth 86¢ instead of $1.25. But the taxes don’t affect your results at the bottom of the pay table: If you win a Three of a Kind and get your wager back, you haven’t really won anything, and your gambling income would be zero. If you fail to make a paying hand and lose your original $1.25, taxes won't affect the results either, because you can't deduct your gambling loss.

Looking at the probabilities, in 55% of hands you’d fail to make a hand, and the loss is all yours. In 28% of hands you’d end up even. In the other 17%, you’d end up winning something, and the governments want their shares.

When I added up the adjusted wins, instead of a 0.76% edge in your favor, I found that you expect to lose 16.59%. Worse than the horrible tie bet in baccarat, and three times worse than the odds of the double-zero roulette. (Those bets are still bad, and become even worse when you consider the effect of the asymmetrical taxation I just described.) You’d not even dream of playing a game where you expect to lose 16.59% of your bet, would you?

So, you thought you had a 0.76% edge in your favor, but it’s really a 16.59% edge against you. The casino doesn’t have an edge either: it also expects to lose 0.76% to your perfect play. It’s the governments that have an edge here! Even ignoring the taxes the casino pays if and when it wins your money, the state and federal governments have a 17% edge in this bet.

Careful readers would notice a problem with my argument above. We only calculated the edge for a single bet, but you are not taxed on each individual bet. Rather, you are taxed per session, which could consist of several bets. When you make many bets, the range of possible results becomes less varied, and the mathematical variance (relative to all the money that you have put at risk) becomes relatively lower.

So let’s assume you make two bets instead of one. About 30% of times you’d lose both your bets. And in 31% of cases you'd lose one of your two bets and get the other back through a Three of a Kind, thus losing half your total wager. At other times, you’d end up flat or you'd win something. Overall, the average amount of money you may end up losing would be reduced. If you lose overall, you’d be on your own to cover your loss (in other words, you can't lower your taxes due to the loss). If you add the numbers up, playing two hands reduces your expected loss from 16.59% of your total wager for one hand to 13.71% of your total wager for two hands, according to my calculations.

Playing more hands in a session will reduce the expected loss even further. Playing ten hands results in a 7.26% expected loss, fifty hands gets you to a 3.68% loss, and a hundred hands to 2.71%. I ran the numbers up to a thousand hands, but even then, you should expect to lose 0.92% of your total wager!

Now, I only had a limited amount of time to run my calculations. There may be a certain number of hands that, if you play that many hands in a session, you would finally have an edge. But the numbers I’m showing above should be quite eye opening. (They'd be even worse if you are in a higher tax bracket.)

Let’s look at them again: you planned to play a thousand hands of your Full Pay Deuces Wild in a session. You expected to wager a total of $1250, you expected to win $9.52, and you assumed the government would take some of that. You thought you still had a positive expectation. But when you consider your taxes properly, even with perfect play, the actual expectation is losing $11.50 in your one-thousand-hands session. If the casino is not compensating you that much in comps, you’re better off not playing. (Why would the casino put up a game with a 0.76% edge against them and comp players 0.92% on top of that is beyond me, but I guess it could happen if there's an amazing promotion. If you run into such a game, be careful and calculate the value of promotions correctly. The car they’re giving as a prize comes with a tax bill too!)

So, with the latest tax law, can you actually expect to make some money gambling if you have a well-paying day job and you’re not filing taxes as a professional gambler? Yes, but only if you have a large edge, or there's something that covers your losses (like a coupon or an existing win):

- You have free play from a coupon with no requirements for betting your own money (like some of the coupons from the Las Vegas Advisor or the American Casino Guide)? You almost definitely have an edge because there’s no chance for a loss.
- You have a matchplay coupon? Because you are risking some of your own money, you need to do your own math based on your marginal tax rates to see if it’s worth playing. If your total marginal tax rate is not too high, it may be worth playing since match play coupons tend to come with a large edge against the casino.
- You’ve already won more money than you lost in this session from a coupon or free play? You can play any game with a theoretical edge while you are still in black, since losses can now reduce your taxes until you wrap up your gambling session. But you should stop betting if you lose the money you had won, or if your gambling session ends.

Finally, there is a chance that a tax-adjusted strategy could do slightly better than the commonly available strategies (which don’t consider taxes): If by changing the strategy you can reduce the number of hands with no pay, perhaps you can reduce your expected loss. I don’t have the tools to calculate such a strategy for a long session, but we can do that for a single bet using the Wizard Of Odds calculator. If I put the tax-adjusted return (based on the tax scenario that I mentioned above) for each bet into the calculator, the calculated strategy would have a 16.58% expected loss instead of 16.59%. Someone smarter than me can try to come up with a strategy that is optimized for a session of several wagers, but I believe the longer the session, the closer such a strategy would be to a commonly available strategy.

The main point that I tried to highlight in this post is that if you have other sources of income and are not filing your taxes as a professional gambler, you need to understand your taxes and consider your marginal tax rates in order to find out if you have an actual edge. This is much more important now that itemizing deductions is not as beneficial as it used to be.

(Originally posted by the author on the Wizard of Vegas forum in December 2019)

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