Wizard
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Wizard
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November 24th, 2021 at 6:56:25 PM permalink
Quote: Hunterhill

So if you had ace ten suited you could still get a royal after throwing the ten away.
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Yes.
It's not whether you win or lose; it's whether or not you had a good bet.
drrock
drrock
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November 24th, 2021 at 7:01:45 PM permalink
Quote: Wizard

Quote: heatmap

Are there no other poker games out that that use some kind of multi deck way of playing the game?

Are single video poker games limited to one deck per game legally?
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The only thing close to a multi-deck video poker game I have ever heard of is Five Deck Frenzy, where all five positions where dealt from a separate deck. I think this game went the way of the dodo bird in the 70's or 80's. However, you can still find a booklet on the game at the Gambler's General Store.
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Hey Wiz, you actually did a similar analysis some years ago on a Cryptologic game that you categorized under the name "Bonus Video Poker." It is listed on your page of video poker games:

https://wizardofodds.com/games/video-poker/tables/bonus-video-poker/

These games had what you dubbed a "redraw bonus" that, in the event that you redrew a discard, paid some percentage of the bet back, varying from 16% to 22% of the bet.

There are a couple features of having a chance at getting discards back. The first is that there are no penalty cards. Basic and Perfect Play strategy should be equivalent. In non-kicker games with a redraw bonus, dealt quads should always involve holding 4 cards rather than 5 since you have a chance at getting the discarded 5th card back on the draw.
ThatDonGuy
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November 24th, 2021 at 7:13:07 PM permalink
Quote: Wizard

The analysis was not as hard as I thought. Here is what I have for 9-6 Jacks how this game is played.

Hand Pays Combinations Probability Return
Royal flush 800 734,636,352 0.000022 0.017402
Straight flush 50 3,514,720,736 0.000104 0.005203
Four of a kind 25 73,614,865,896 0.002180 0.054492
Full house 9 378,547,499,304 0.011209 0.100877
Flush 6 366,123,839,872 0.010841 0.065044
Straight 4 371,569,671,840 0.011002 0.044008
Three of a kind 3 2,402,049,989,664 0.071123 0.213370
Two pair 2 4,354,485,731,856 0.128934 0.257868
Jacks or better 1 7,014,355,671,540 0.207691 0.207691
Nothing 0 18,807,968,780,940 0.556894 0.000000
Total 33,772,965,408,000 1.000000 0.965957


As a reminder, the return of fair 9-6 Jacks is 99.56%. That makes the cost to putting the discards back in the deck 2.95%. I'd love for one of the math geniuses of the forum to confirm or deny this table.
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I don't know about the individual rows (not yet, anyway), but I also get 96.5957% as the ER for 9/6 Jacks or Better.
Wizard
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Wizard
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November 24th, 2021 at 7:41:52 PM permalink
Quote: drrock

Hey Wiz, you actually did a similar analysis some years ago on a Cryptologic game that you categorized under the name "Bonus Video Poker." It is listed on your page of video poker games:

https://wizardofodds.com/games/video-poker/tables/bonus-video-poker/

These games had what you dubbed a "redraw bonus" that, in the event that you redrew a discard, paid some percentage of the bet back, varying from 16% to 22% of the bet.

There are a couple features of having a chance at getting discards back. The first is that there are no penalty cards. Basic and Perfect Play strategy should be equivalent. In non-kicker games with a redraw bonus, dealt quads should always involve holding 4 cards rather than 5 since you have a chance at getting the discarded 5th card back on the draw.
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You have a very good memory. I 99.54% forgot that game. This looks like that game, with no redraw bonus.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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November 24th, 2021 at 7:42:37 PM permalink
Quote: ThatDonGuy

I don't know about the individual rows (not yet, anyway), but I also get 96.5957% as the ER for 9/6 Jacks or Better.
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Thank you for the confirmation, Don. You're the best!
It's not whether you win or lose; it's whether or not you had a good bet.
ThatDonGuy
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rsactuarymipletDeMangoAxelWolfgordonm888
November 24th, 2021 at 7:44:09 PM permalink
Quote: Wizard

Quote: ThatDonGuy

I don't know about the individual rows (not yet, anyway), but I also get 96.5957% as the ER for 9/6 Jacks or Better.
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Thank you for the confirmation, Don. You're the best!
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I know
Wizard
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November 25th, 2021 at 3:43:21 AM permalink
The following return table is based on following optimal strategy in fair 9-6 jacks, but actually playing the cheating game.

Hand Pays Combinations Probability Return
Royal flush 800 767,547,516 0.000023 0.018181
Straight flush 50 3,524,021,144 0.000104 0.005217
Four of a kind 25 73,598,753,592 0.002179 0.054481
Full house 9 378,491,782,968 0.011207 0.100863
Flush 6 362,727,142,360 0.010740 0.064441
Straight 4 371,824,584,732 0.011010 0.044038
Three of a kind 3 2,401,771,851,648 0.071115 0.213346
Two pair 2 4,354,714,729,872 0.128941 0.257882
Jacks or better 1 7,007,119,858,020 0.207477 0.207477
Nothing 0 18,818,425,136,148 0.557204 0.000000
Total 33,772,965,408,000 1.000000 0.965925


Interestingly, the return is only 0.000032 less than the table based on optimal strategy for the cheating game.

The difference between this return and fair 9-6 jacks return is 0.029514.
It's not whether you win or lose; it's whether or not you had a good bet.
3for3
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November 25th, 2021 at 7:15:10 AM permalink
That makes sense to me. I am struggling to come up with a hand that should play differently, armed with the knowledge that we might get a discard back.

Ok, I think I might have one. RF3 with AT, vs FL4. I know the play is close, since a penalty card will flip the play from one to the other. It might be the case that we always hold the FL4, since it only needs to catch one, instead of the RF3, since our chances of hitting the royal have gone down a fair bit, and that is a huge part of the return.

If you could compare the 2 and show us which, I'd be interested from an academic POV.
DRich
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heatmap
November 25th, 2021 at 7:48:48 AM permalink
I actually think it is a smart way to design a video poker game. It is definitely misleading for traditional video poker players but I would not consider it cheating. You could advetise your games as having good familiar paytables but hold a few extra percent. It should definitely be disclosed in a rules screen.
Order from chaos
Dieter
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November 25th, 2021 at 10:50:43 AM permalink
Quote: DRich

It should definitely be disclosed in a rules screen.
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Absolutely.
If they tell you how they deal the game, then deal as announced, it probably isn't cheating.
May the cards fall in your favor.

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