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robomb162
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April 10th, 2021 at 1:57:12 PM permalink
This website and forum is simply amazing. The sheer amount of data available is astounding. I am wondering if anyone here can help me out with this.

We have a video poker game here called "Aces Live" that has a live dealer dealing from a deck of 6 cards. You then choose which cards you are going to hold. The dealer deals out 5 new cards and any cards in the spots you did not hold are replaced. So essentially, this is just normal 5 card draw with 6 decks of cards. That means you can get repeated cards, pairs and trips are much easier, and 5 of a kind is possible.

Here are the payouts:
Royal Flush 250
Straight Flush 50
Five of a Kind 50
Four of a Kind 10
Full House 8
Flush 5
Straight 3
3 of a Kind 2
Two Pair 1

Is there another variant existing on this site that is similar to this I can use to devise a strategy? If I stick to the Jacks or better strategy will that be close enough, or should I look at something else? Or, if I'm not stepping too far asking the more difficult questions: What is the return rate of this game? What should my strategy be? (or if it's easier, What strategy adjustments to a different video poker game should I make to create a solid strategy?)

A related question: There is going to be a tournament of this game. Up to 60 players will play per round and the top 10 advance to the next round. If everyone starts with say 300 credits, at what credit level could I stop playing (or maybe just reduce my bet size) because I can reasonably expect I would be in the top 10? Let's say I have no information about other players' results, everyone plays up to 20 hands, and everyone plays slightly (maybe 1%) below perfect strategy. Does this answer change much if the average player plays at a strategy 5% below perfect strategy?

Feel free to make any generalizations to give a useful answer. I just have no idea how to even start answering the question in the last paragraph.
Mission146
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April 10th, 2021 at 2:48:25 PM permalink
I'll PM Wizard for you if nobody does this in the next day or two. He might be interested enough to make a page out of it, but he's probably going to want you to identify where this game might be found.

I'm not even going to lie...not only would I not come up with a return percentage on this one for free---but it's probably a good measure out of my league anyway. I could determine optimal decisions on individual hands...pretty easily, in fact, but I don't think I could come up with an overall expected return.

In terms of strategy, here are my one minute intuitions:

1.) Flush draws will become much more valuable because flushes on the draw become significantly more likely.

2.) Even though the Royal Flush only pays 250:1, I'd assume that you'll be more aggressive in those holds as they also become more likely...and those Royal holds that are also a three-flush have it more likely to catch two for the flush.

3.) Same as #2, but with straight flushes.

4.) All pairs are equal. Based on the paytable, I'd think that a four flush beats any single pair. I know four flush beats a non Jacks+ Pair in Bonus Poker Deluxe---which pays more on both the 3OaK and 4OaK than those hands pay here. 5OaK is possible in this game, but pays less than any quads in Bonus Poker Deluxe---so I tend to think four flush is always the hold over a pair.

5.) I'm not sure about open-ended straights v. a single pair, but I can do the math on that easily enough, if you want.

The opening rounds of tournaments like that, I tend to think you just want to be aggressive. I can't really suggest any particular, "Stop point," without seeing the game in action. Sixty players each playing twenty hands...I figure at least ten would have more than they started with.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
robomb162
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Mission146
April 10th, 2021 at 3:01:13 PM permalink
The game can be found at Running Aces Casino in Minnesota. If there is anything else I should add, please let me know.
GaryJKoehler
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April 11th, 2021 at 6:09:41 AM permalink
This would be a herculean analysis. Even using the Wiz’s super-fast methodology:

https://wizardofodds.com/games/video-poker/methodology/

With it one would first have to loop through Combin(312, 5) = 23,856,384,552 hands and store scored results in arrays of sizes 23,856,384,552, 387,278,970, 5013320 and smaller. Then one would have to loop through all the unique hands taking the 24 suite permutations into consideration evaluating each of the 32 possible holds per unique hand. For a normal 52-card games, this is 134,459 hands. Not sure what it is for this game.

The 23 trillion in the first step is a show-stopper.

A 2-deck version would “only” need 91,962,520 in that first step so is probably doable as an approximation.
GaryJKoehler
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April 11th, 2021 at 11:36:02 AM permalink
I think the number of unique hands with two decks is 152,646.
robomb162
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April 15th, 2021 at 4:58:12 PM permalink
Would you mind talking me through how you would work out #5? I've convinced myself that your one-minute intuitions on basic strategy are correct, but if you could talk me through how you would calculate EV for open-ended straights v. a single pair that would help me know how to work out a few other details.

You can run into interesting situations in this game like: 9c9cTcTs4c. Do I keep the 2 pair or do I keep one pair and go for the flush? I would be fine working out those details myself once I know how to do it.
gordonm888
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April 16th, 2021 at 5:54:52 PM permalink
I have an excel spreadsheet that is a video poker analyzer capable of multiple decks. I could develop strategy using that but I cannot calculate the Return across all hands.

I agree with Mission that flushes will be more common - a three card flush draw will hit about 50% more often than in a 1-deck game.

I am not seeing any reason why a royal or straight flush will be much more common though. The odds of getting each card in a spades royal flush is still 1 out of 52, roughly. In fact, I believe its slightly less probable to get a royal flush with 6 decks than with one deck.

Obviously pairs, two pairs, trips, boats and quads will all occur more frequently. Pairs will be about 30% more frequent and quads will be, I don't know but I guess, about 8X more frequent than in one deck. I think you should be drawing to make trips and quads at every opportunity.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
gordonm888
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April 16th, 2021 at 7:17:10 PM permalink
Here is my rough simple strategy, done in my head, based on the pay table you posted:

1. Obviously, keep any made hand, 2pr or better, and draw cards to it as possible.

2. Keep a flush draw (4 suited cards) and discard the unsuited card.

3. Draw to a pair. If you have both 4 suited cards and a pair, discard the pair and draw to the flush.

4. Draw to an open-ended straight.
- if you have an open-ended straight draw and a pair, draw to the pair.

5. If you have a garbage hand -no pairs, flush draw or straight draw, discard 4 cards. Keep 1 card, preferably in the range 5-10, with as few straight blockers and flush blockers in the four cards you are discarding.

Never discard all 5 cards.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
GaryJKoehler
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April 17th, 2021 at 10:48:11 AM permalink
Quote: GaryJKoehler

I think the number of unique hands with two decks is 152,646.


With further work, I believe the number is 202,735. Just wanted to correct that.
GaryJKoehler
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April 17th, 2021 at 12:39:21 PM permalink
And the 23 "trillion" should have been 23 "billion". Bad counting day!
Wizard
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April 18th, 2021 at 5:58:21 AM permalink
I just found this thread. This would make for a good challenge. However, this would take a lot of recoding of my video poker program and I don't have time right now. Even if I did it, I would only get an optimal strategy return, but without a strategy. It looks like one of the other math geniuses of the forum might take this on.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
robomb162
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April 18th, 2021 at 4:26:24 PM permalink
Just for reference, my group of 3 played in the tournament today. With the help of this thread we had a 4th place and an 8th place finish and qualified for the championship round (on top of $200 for 4th place and $50 for 8th place). The distribution of final scores was pretty interesting:

Starting balance - 300 credits (you had to play at least one hand), minimum bet 2, maximum bet 10

1st - 420
2nd - 380
3rd - 380
4th (my wife) - 361
5th - 330
6th - 320
7th - 312
8th (me) - 308
9th - 300
10th - 300
20th - 220
30th - 168
40th - 50

When my wife hit 370 with 2-3 minutes remaining I was screaming at her to switch to min bets (I should have told her to just stop playing at all). I was at 320 with about 90 seconds left and switched to min bets from that point on. We were at a huge disadvantage because we were in the first group of 6 (out of 50-60 players total throughout the day), and the leaderboard was updated after each group. It is incredibly advantageous to be in the last group. I didn't count how many hands we played since I was making sure I didn't make any huge mistakes while still playing quickly, but my guess is got in about 30 hands in 10 minutes. It's actually a pretty genius system the casino came up with to get around legislation in our state (video poker technically isn't allowed, so the live dealer gets around the rules).

I'll definitely put in some more study before the championship round. The championship round has 90 players in 9 different randomly chosen heats of 10 players/heat. Payouts are only for the top 10:

1st - $4000
2nd - $2500
3rd - $1500
4th - $1000
5th - $500
6th through 10th - $100

It seems here the strategy is to play for a top 5 spot instead of a top 10 spot because of the huge pay jumps. Based on what I heard and my observations of the score distributions, my strategy going into the event will be to stop playing if I hit 450 (I'll adjust if I'm in one the later groups and get to see the scores of other players), but otherwise I will max bet.

By the way, the 3rd in our group thought that Joker Poker is probably the closest game to this game. Does anybody have any thoughts on how accurate it would be to look at EV in different spots using this game?

Thanks again for everyone's help!
GaryJKoehler
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FiliusBruce
April 19th, 2021 at 9:43:21 AM permalink
I realize your interest is in the tournament, but this game presents an interesting challenge to the math guys. For me, this is the only VP game I know of using more than one deck. Maybe there are others? Anyway, I did manage to compute the EV for a 2-Deck version. It is 0.751724 (with standard deviation of 2.08198). I don’t know if it gets better for more decks. The single deck version has an EV of 0.528373 (with standard deviation of 1.81981). I’m not surprised it is so low given one of the main payouts (for Five of a Kind) would never be realized and all the other pays are lower than, say, for 9-6 Jacks or Better.

To compute the EV for more decks is beyond my toolset – the arrays needed are just too big for my compiler. This game would make an interesting base for a different computational approach for Video Poker games than the ones we normally take.
unJon
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April 19th, 2021 at 10:02:01 AM permalink
Quote: GaryJKoehler

I realize your interest is in the tournament, but this game presents an interesting challenge to the math guys. For me, this is the only VP game I know of using more than one deck. Maybe there are others? Anyway, I did manage to compute the EV for a 2-Deck version. It is 0.751724 (with standard deviation of 2.08198). I don’t know if it gets better for more decks. The single deck version has an EV of 0.528373 (with standard deviation of 1.81981). I’m not surprised it is so low given one of the main payouts (for Five of a Kind) would never be realized and all the other pays are lower than, say, for 9-6 Jacks or Better.

To compute the EV for more decks is beyond my toolset – the arrays needed are just too big for my compiler. This game would make an interesting base for a different computational approach for Video Poker games than the ones we normally take.



You could probably do an infinite deck calculation to bound the top end of the EV.

My gut is that infinite deck strategy would be accurate except in very close calls.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
GaryJKoehler
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April 19th, 2021 at 10:20:09 AM permalink
Makes sense.
GaryJKoehler
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April 19th, 2021 at 10:30:27 AM permalink
Like the 6-Deck version, an infinite deck would have only 208,481 unique hands up to position and suit permutations. So the EV could be computed fairly easily, in principle.
robomb162
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April 19th, 2021 at 11:08:24 AM permalink
Quote: unJon

You could probably do an infinite deck calculation to bound the top end of the EV.

My gut is that infinite deck strategy would be accurate except in very close calls.



This is more or less what I've been doing in my estimates for strategy decisions. I tried to calculate EV by assuming all current cards were replaced in a 52-card deck, even if I held those cards. It seems like a close enough approximation, and on close decisions could always be compared to a one-deck or two-deck analysis.
gordonm888
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April 20th, 2021 at 8:37:12 AM permalink
If you're discarding 4 cards and drawing to a J-A, then 1/4 of the cards that you need to get a pair have been removed from the deck.

If you are drawing three cards to a pair, 1/2 of all the cards you need to make trips are removed from the deck.

Ignoring card removal will not give you a decent approximation. It will be way off.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
unJon
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April 20th, 2021 at 8:41:19 AM permalink
Quote: gordonm888

If you're discarding 4 cards and drawing to a J-A, then 1/4 of the cards that you need to get a pair have been removed from the deck.

If you are drawing three cards to a pair, 1/2 of all the cards you need to make trips are removed from the deck.

Ignoring card removal will not give you a decent approximation. It will be way off.



I don’t follow. If you are drawing to JJ, then 2 of 24 Jacks are missing. How is that 1/2 of the jacks needed to make trips?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
GaryJKoehler
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FiliusBruce
April 21st, 2021 at 4:19:33 AM permalink
Here is an infinite deck approximation of the Aces Live game. If anyone sees a flaw in the approach, please advise.

First I found the frequencies of each of the 208,481 unique poker hands in the 23,856,384,552 hands of the 6-deck game. Both types of hands ignore the position of a card. The unique hands ignore suit permutations. Sorted, the unique hands (with frequencies) look like:

24: A Clubs, A Clubs, A Clubs, A Clubs, A Clubs
360: A Clubs, A Clubs, A Clubs, A Clubs, 2 Clubs

16200: K Clubs, K Clubs, K Diamonds, K Diamonds, K Hearts
12960: K Clubs, K Clubs, K Diamonds, K Hearts, K Spades

Next, for each unique hand I computed the EV of the 32 possible holds completing the draws using an infinite deck. The highest EV hold was found and weighted by its 6-deck frequency to compute the overall game EV.

So computed, the game EV was 0.961642. As unJon surmised, this is an upper bound to the actual 6-deck EV.

One interesting point, with an infinite deck the EV of a no-hold hand is the same for all starting hands, thus simplifying the hardest part of the calculations. It just has to be done once. This is true for each of the 52 1-card holds, simplifying the second hardest part of evaluating holds of a hand.
camapl
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June 29th, 2021 at 1:33:24 AM permalink
Is each hand dealt from a freshly shuffled shoe? If not, this would have a huge impact on subsequent hands…

Also, are cards dealt face up? If so, this would add another level of complexity to an already lengthy strategy.

Would love to hear how you and the wife fared in the finals!
Expectation is the root of all heartache.
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