Practical quesetion: 3 to Royal or 4 to flush?

So I was doing some math today on Video Poker and ran into an interesting situation.

It's 9/6 JOB (the concept could apply to other video poker as well), I got 3 to royal with an ace and a ten, another card of the same suit, and a random non-blocker (such as Ad, Kd, Td, 4d, 2s).

I ran it through the calculator and it suggested the optimal play is keep 3 to royal with an EV of 6.434 per 5 units bet, and the runner up is 4 to flush with a EV of 6.383

That is a difference of only 0.012 EV per unit

So that makes me wonder, if going for royal here is indeed the correct play. Because if god forbid, you hit that royal (I've never hit a royal in my life on 1 line), you'll get taxed and you're "supposed" to tip, not to mention the exact thing you're tipping for - hand pay - is going to inconvenience you and waste maybe a good half an hour of your time.

In addition, going for 4-flush also significantly reduces variance. Usually reducing variance is desirable.

So with all that in consideration, is it still the best play to go for 3 to royal? What do you guys think?

Personally after contemplating that I've decided that small EV gain is not worth the negative sides of hitting a royal. So from now on I'm keeping 4-flush in a situation like this.

I always follow optimal strategy for 9/6 JoB. So in this case, I go for the royal. Now if the hand is Ah, Jh, 10h, 4h, Kc, I'm going for the flush instead.

It's up to you, really. I don't think holding the 4-flush is an awful play, when you take in the other considerations (variance, hand-pay, slow down play, etc.).

It depends on the game.

Jacks or Better, 8/5 or worse: keep the 3/Royal.

Jacks or Better, 9/6 or better: if the 3/Royal includes both an Ace and a 10, keep the 4/Flush; otherwise, keep the 3/Royal.

9/7/5 Bonus Poker: keep the 3/Royal only if it's K Q J or Q J 10.

Quote: ThatDonGuy

...Jacks or Better, 9/6 or better: if the 3/Royal includes both an Ace and a 10, keep the 4/Flush; otherwise, keep the 3/Royal...

Almost. This depends on the other two cards. In order for the four card flush draw to be correct, one of the others must be the same suit and the other must be a 10 or missing straight card.

Example Ah, Jh, 10h, 4h, Ks = flush draw. Ah, Jh, 10h, 4h, 6s = royal draw.

You guys don't mind getting taxed on the royal? I'm not sure how to do the calculation here but my instincts tell me the taxes alone may offset the EV difference from 3-royal.

Quote: Neutrino

You guys don't mind getting taxed on the royal? I'm not sure how to do the calculation here but my instincts tell me the taxes alone may offset the EV difference from 3-royal.

Most are losing gamblers anyway. Just write it off and you'll owe no taxes.

Also, quarter royals aren't taxed...yet.

According to the Wizard's analyzer, https://wizardofodds.com/games/video-poker/hand-analyzer/

Holding the 3 to a Royal is worth 1.286 while holding the 4 to a Flush is worth 1.276

So, yeah, it's kind of a coin toss...

It is no coin toss when taxes are taken into effect and you do not itemize. Take the 4 to a flush.

Why even play if you don't want a royal? Makes absolutely no sense.

After giving this a re-think, it occurs to me that the calculator is assuming betting max credits. How much different are those numbers if you're betting less than max coin?

Additionally, holding the 3 to a Royal is worth more because drawing two cards increases the chance of getting any type of win.

So, if you factor that in, as well as the tax and tip issue, it just might be better to hold the 4-flush.

When not betting max or if you're on a machine where the royal pays 500/1000/1500/2000/2500 like this:


then the four flush wins.

I think one should always play on max coins. Might as well switch down a level if you can't afford the variance. As in It's better to play 9/6 JOB on 5c max coins than 9/6 JOB on 25c 1 coin. It's almost exactly the same except the royal payout.

Quote: Ibeatyouraces

I always follow optimal strategy for 9/6 JoB. So in this case, I go for the royal. Now if the hand is Ah, Jh, 10h, 4h, Kc, I'm going for the flush instead.

I think I got Mission and a few people on that hand after the nugget challenge when someone said they knew 9/6 perfectly. Most people automatically say the 3RF.

Quote: DJTeddyBear

After giving this a re-think, it occurs to me that the calculator is assuming betting max credits. How much different are those numbers if you're betting less than max coin?

Additionally, holding the 3 to a Royal is worth more because drawing two cards increases the chance of getting any type of win.

So, if you factor that in, as well as the tax and tip issue, it just might be better to hold the 4-flush.

This scenario actually came up recently for someone who was playing with me. I did tell them to hold 4 flushes over 3 card royals, but there was "extra value/reasons" for doing so. It was an obvious decision.

The person playing should make the decision themselves during play based on how much losses/wins they already have for the year. Depending on and how much you tip, that's also going to factor in.

Personally I try to avoid playing anything where something like that really makes a difference. IMO if you're putting in enough time on something where you really need to worry about this, then you're probably on the wrong path.

How often does it actually come up and make a difference?

It may be interesting to talk about. Hopefully It's not something you truly have to worry about.

Quote: AxelWolf

I think I got Mission and a few people on that hand after the nugget challenge when someone said they knew 9/6 perfectly. Most people automatically say the 3RF.

For some reason I always remember that rule. It will save me a penny over my lifetime. I really wish I remembered more important things...

Mission146 holds four to a straight with no high cards over a pair! :P

Quote: teddys

Mission146 holds four to a straight with no high cards over a pair! :P

Used to, anyway.

Quote: teddys

For some reason I always remember that rule. It will save me a penny over my lifetime. I really wish I remembered more important things...

Mission146 holds four to a straight with no high cards over a pair! :P

During long plays, progressives, promotions or whatever with friends or other pro's, sometimes you talk about interesting holds and things like that.

IMO that's the best way to learn/refresh strategies (aside from making them yourself). It's like poker players talking about percentages and game theory. Never be embarrassed to ask you're friendly neighbor if you forget or don't know.

Quote: Neutrino

Personally after contemplating that I've decided that small EV gain is not worth the negative sides of hitting a royal. So from now on I'm keeping 4-flush in a situation like this.

I came to the "keep 4 to a Flush" conclusion when I was playing $ 1 9/6 JoB at CET with a goal of getting to Diamond Status.

I do enjoy the Diamond Lounges in Vegas.

And yeah, the $ 1 9/6 JoB got yanked (not because of me) from my home Casino. They got yanked because CET are greedy bastiches. ROMES knows what I am talking about.

Quote: teddys

For some reason I always remember that rule. It will save me a penny over my lifetime. I really wish I remembered more important things...

Mission146 holds four to a straight with no high cards over a pair! :P

Quote: Mission146

Used to, anyway.

It's correct when the straight pays 5...lol

As for the question, I think I've ran across the exception maybe once or twice. But yeah, considering taxes, you can probably argue 4 to a flush with AHT suited in this spot.

I think the choice to go for a royal is one only you can make. In my case, I've had one on quarters, and a progressive on a $2 which hit for $11355. My AGI last year was about 25k, but I took a new job last November which has thus far paid me 36k - and I expect at least another 4k in commissions between now and year end.

In the US, and also being in Alabama, I have state tax to worry about, too. So - I set aside 25% of it just for taxes. It's earned me a whole 60 cents so far!

I see little problem with taking 25% of a big chunk of cash that I didn't have before to pay taxes on. The rest, I maxed out my IRA to reduce my tax bill as much as I can. I might have to pay some for Alabama state, but I think that 25% I set aside will go straight in my IRA for next year, because even at 40k Gross- after deductions, I'll still be in the 15% bracket. Given deductions, exemptions and what's withheld already, I'm not worried about it in the least.

Paying taxes is a good thing. It means you made money.

Paying less taxes having made more money is even better.

If I can get the tax loss statements from all the casinos, I should be quite alright.

For me, I'll go for the royal pretty much every time.