Assume you are a 5-coin dollar player playing 9/6 Jacks or Better and are dealt 3♠ A♥ K♥ T♥ 5♥. The only two plays to consider are holding three hearts to the royal flush and holding all four hearts.
If we check out EV, we find holding three hearts is worth $6.43 and holding four is worth $6.38. That nickel’s worth of EV has always been too much for me to ignore and I go for the royal every time.
BUT, I file as a professional player and get lots of W-2Gs. Let’s say you don’t get a lot of W-2Gs. In that case, each one that you do get has some serious tax consequences. What if you held the four hearts in order to prevent the W-2G?
Once every 1,081 times on average, AKT turns into a royal flush. If you gave up a nickel each of those 1,081 times and ended up getting one fewer royal flush, it would cost you $55 (rounding slightly).
This is probably not too high a price to pay because a $4,000 royal has far more than $55 worth of tax consequences.
AKT (and AQT and AJT) are the weakest 3-card royal flush draws for two separate reasons. First, the presence of the ace eliminates all straight flush possibilities and reduces straight possibilities. Second, the presence of a ten reduces the chances for a high pair.
If we compared the preceding hand to 3♦ A♣ K♣ J♣ 5♣, holding this 3-card royal flush is better than the 4-card flush by a little more than 17¢ and avoiding the $4,000 royal flush over 1,081 opportunities will cost you $185. That’s quite a bit more than the $55 we were talking about earlier.
Going for the flush from 3♥ K♠ Q♠ T♠ 5♠ costs us $683 over the 1,081 draws, and from 3♣ K♦ Q♦ J♦ 5♦, it sets you back $770. Finally, from 3♠ Q♥ J♥ T♥ 5♥ you’ll lose a whopping $1,095 over the 1,081 hands by going for the flush every time.
So where do you draw the line? I’m not sure. I go for the 3-card royal on all of these hands. You’re going to have to decide for yourself what avoiding a W-2G is worth.
Other factors: If it were a multiple point day and/or there was another juicy promotion which gave me a considerable advantage playing this game, I would be more inclined to go for the flush. After all, time is money and it could easily take 5-20 minutes to be paid.
If I were playing in a state where royals were penalized (say Mississippi which has a 3% non-refundable tax on W-2Gs), that would make going for the flush mandatory in our first example and a closer play in the others.
If I were playing near the limit of my bankroll — either actual or psychological — I would tend to go for the flush, which is a play with a much lower variance.
On the first hand, you get skunked about 70% of the time going for the royal and “only” 68% of the time going for the flush. If I were someone for whom today’s score mattered, I might go for the flush. I certainly don’t recommend that you worry about today’s score, but some players just can’t help themselves.
This wouldn’t happen to me because I don’t do this, but if you were picking up someone else’s free-play and a royal flush would be awkward and you insisted on playing dollars anyway because you were in a hurry, I would go for the flush every time on these hands.
There are other hands in this game and every other game where it could make sense to avoid the possibility of a royal flush if it could be done at a low cost. But you should look at them one-at-a-time BEFORE YOU PLAY so you know which “inferior” plays are cost-effective. Trying to figure it out at the machine is very difficult. It’s easy to over-compensate when you’re doing this without study beforehand.
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I appreciate this very in depth column that covers a deal situation for novice players. Thank you Mr. Dancer.
I’m only a quarter player when just “playing” so I always take the optimal play. Now if I’m vulturing games, then I might have to make drastic measures if I’m in a location where I’m “not welcome.”
Of course, the attendant question should be asked: at what point does tax liability wipe out positive EV when you’re playing at these stakes? Yes, of course you would be reporting NET wins, but for someone who doesn’t file as a Schedule C professional gambler, the IRS will assume that every W2-G represents an actual win for the entire gross amount! YOU know that you were down $3800 when you hit that $4000 royal, but THEY don’t care about facts. So a recreational player hitting a royal at stakes higher than .25 will incur an (unfair) tax liability that will make the game not have been worth playing, no matter how good it ostensibly was in terms of EV.
Great article. I am a California resident and the tax bite is to much on W2-G earnings. I was looking forward to seeing you address this dilemma in an article and you did. Great info for those of us that are not professional players, but do like play for maximum EV.
Hii Bob, thanks for all you do. I have all of your books.
I am suprised you did not mention line 4 from your JoB advanced strategy in your book:
RF3……….{AHTx when the fifth card is T, J, Q, or K}
I forgot the “less than” symbol.
This article wasn’t at the advanced level. A discussion of penalty card considerations would render the column too complicated for many of the readers I was trying to reach.
Just wondering , what would you do if your playing someone’s else’s free play and your dealt a royal? I realize this doesn’t happen very often.
Wouldn’t happen to me. I don’t pick up anybody else’s free play — simply because I assume that somebody in executive row in every casino I play at wants to kick me out and i go out of my way not to give them any reason to do it.
If somehow i HAD to pick up somebody’s free play (I don’t see how this could happen — but just saying ) I’d do it at single-line quarters and a $1000 jackpot wouldn’t cause the machine to lock up. I’d just keep going.
Great advice, Bob – you’re the best!
I come up with $575 as the cost for KQT5s3h.
Another way I look at it is how much it costs to hit the royal, how much of a margin it is, and if I’d want to let a computer run indefinitely with my money on the line with that kind of margin. Even without any costs besides the machine, I’d feel nervous about paying $3945 to hit each $4000 royal, considering how much fluctuation is involved. I’d never want to play a game with that little overall margin.
Kevin , in the U.S.as a recreational player you add $4000 to your gross income and then remove $3800 under miscellaneous deductions giving you a net taxable of $200 unless of course you have other losses which could wipe that out as well.
Good reply. I am worried that President Trump’s proposal to eliminate all deductions except mortgage interest and charity giving would seriously impact the real estate business in the high tax states and effect the gaming business. I know personally, I would have to modify my approach to the game to avoid those W2Gs on the games I currently play.