3 Way Action Video Poker

I have been playing 3-Way Action Video Poker off and on for 15+ years and really enjoy the game. I play only the 99.291% version discussed at the Wizard of Odds and use the Wizard's strategy for that game. However, the 99.291% game is somewhat rare, at least in the 25c game, which I prefer. I saw the Wizard's update on this game (as of January 20, 2019), which discusses 5 separate paytables. However, the version I see most frequently is NOT included. That version maintains the same paytable on both the 5 Card Dealt hand (97.041% payback) and the 5 Card Draw Hand (9/6 Double Double Bonus). However, the 7 Card paytable eliminates the 2 pair (J-A up), and instead, doubles the pay on 4 of a kinds (and increases Full House pay from 4 to 5)---which is the same 7 Card paytable you show for the 9/5 Double Double bonus paytable. Since that paytable is extremely common at the casinos I frequent, could you calculate the payback on that version? My assumption is that it's not quite as favorable as the 99.291% version and I estimate it to come in at somewhere between 98.7% and 99.0%. In addition, I would love to see the strategy for that version. I'm sure I'm not the only one interested, as I have seen a lot of comments on other forums regarding this version of the game (and the games get a lot of action). Thank you.

The Wizard has said on at least two occasions that this game is among the most difficult that he has analyzed, so don't expect any new information soon. He has other mountains to climb, I'm sure.

According to the game selections in my IGT 3 Way-Action Poker chipset, there's no payable that's between 98.7%–99.0% — I see 97.1%, 97.3%, 97.8%, 97.9%, then 99.1%.

Thanks for you comment. I did read how difficult this game was to analyze on the "Wizard of Odds" website---something like 3 quadrillion possibilities (which he first posted about 17 years ago, or so), but I was hoping that advances in technology might make it a bit easier now, in light of the Wizard's 2019 update where he noted paybacks for 5 or 6 other pay schedules. My quandary is that I know the strategy he shows on the Wizard of Odds website is geared to a paytable that is pretty much non-existent in casinos, and I don't dare play the game using that strategy because the payback is already not that great. Too bad, it is really a fun game.

Thank you for the post, QG, and welcome to the forum! If you play 3-Way Action, then your moniker fits - you hit quads a lot more often on a 7-card game…

Yes, unfortunately it would be quite a feat to rerun the analysis. At least we have something to work with! Using the combinations in the analysis on WoO (thanks Wiz!), I show the following returns for the 7-card portion of the bets:

With RF = 200 * bet portion, the 7-card return = 101.8220%
Full table: 4,000 / 2,000 / 800 / 400 / *200* / 25 / 80 / 40 / 20 / 5 / 3 / 2 / 1

With RF = 160 * bet portion, the 7-card return = 101.1609%
Full table: 4,000 / 2,000 / 800 / 400 / *160* / 25 / 80 / 40 / 20 / 5 / 3 / 2 / 1

Averaging those with the 5-card Deal (97.0414%) and the 5-card Draw (98.1989%), we get overall returns of 99.0208% and 98.8004%, respectively. (Note both pay tables bottom out at 3oak.)

Keep in mind that these would result from perfect play based on the strategy for the higher paying table that includes a payout for 2 Pair (J-A) with the lower pays for the FH’s and standard quads, and also that the Wiz’s strategy was highly abridged for obvious reasons. !!! Over 70K lines of strategy!!!

However, if one were to tweak that strategy *enough* to fit the tables listed above, one could potentially reap higher returns, as optimal strategy for the higher paying table is suboptimal for each of these. It just depends on how much time one is willing to commit.

This was of interest to me at one time, but not *enough*! Although, as you have brought this to my attention again, it occurs to me that we could analyze it a slightly different way… Instead of reinventing the 80-day wheel, perhaps the following method could be a bit faster: if we take the viable holds in the abridged strategy and compare each one by one only with conflicting holds to see which has the higher value most often. Then again, it might be just as much work!

Do any of the bright minds on this forum have ideas to ~estimate~ basic strategy, given a close starting point?

Thank you for your very insightful and detailed response, Camapl. I would be intrigued to see what estimated basic strategy might flow from your suggestions. I certainly hope that there are some "bright minds" who take up the challenge, because I would love to tackle the game if I have a fighting chance at playing at the optimum level.

I get claims of analyzing very rare pay tables throughout my video poker material. In my opinion, there is no sin in that. However, it is a reasonable request to ask me to analyze one that's missing. I will add your request to my list of project ideas. By the way, it always motivates me get a picture of the actual pay table.

Meanwhile, I think it's safe to apply the probabilities to an existing pay table to the requested pay table.

A strategy for this game would be very difficult.

3 Way Action.

Thank you for responding, Wizard. I personally would be thrilled to see your analysis. It may be a month or two before I get back to Vegas (which is the only place I come across 3-Way Action), but I will be sure to take a picture of the pay tables and post it the next time I go.

I spent some time during the pandemic writing a VP analyzer (using lots of tips online from the wizard and others), and then I extended it to this game.
It computes the EV and best hold for every hand. It runs in about 10 seconds on my 12 year old pc.
I'm guessing when the Wizard did this in 2005 and it ran for 80 days it was before he was using some of the optimizations he includes in his "My Methodology for Video Poker Analysis" page.

Using the RF=200paytable you list (and the 9/6 5-card paytable), which is the version I usually play, I have the following for optimal play:
5 card: 0.978151506
7 card: 1.025325700
Add in the deal and you get a return of 99.1297%

As for turning that into a strategy, I wasn't sure of the 'right' way to do that. I hacked something together and massaged that into an 80 line strategy card I use.
There are a lot of strange holds.
- 2-to-SF holds, including A with suited 2-4 (and sometimes A5).
- For high cards, QJ is the only time you hold just 2 unsuited high cards. In general A > QJ > J > Q > K. (The single J,Q drop by one spot if there is a flush penalty.)
- With a single high card that has a flush penalty, you sometimes keep that penalty card. [simple version here is keep penalty card with K, not with Q or J]
- Normally you break aces-full or aces-2pair and keep just the aces, but not if the other pair is 2-4.
- Only 3 SFlush with no gaps (and QJ9) beat a pair of 2-4.
- the ranking of 4-inside straight depends not just on number of high cards, but also number of suits, and where the gap is (ie are there 3 consecutive cards that gives you a chance of getting a straight pulling 2 cards.)

Why isn’t there a 7 card royal flush pay line? Would the hand of suited AKQJT98 be paid as 7 card straight flush?

How much additional return would it add to the game if 7 card royal pay line exists and it pays 8000 for 1?