kubikulann
Joined: Jun 28, 2011
• Posts: 905
September 1st, 2019 at 1:14:43 PM permalink
Video Poker is not popular here in Brussels. One reason is, the best paytable available is .9687EV (3.13% HE).

For mathematical pleasure, I studied the Wizard’s strategy table.
https://wizardofodds.com/games/video-poker/strategy/a-1-b-37-c-1-d-0-d-1-d-2-d-3-d-4-d-5-d-6-d-25-d-40-d-80-d-50-d-800/

Two things intrigue me.
1) why is it that the strategy does not take into account which cards are discarded? Does it mean that the VP machine draws replacement cards from the whole deck - not restricted to the cards not drawn in the first hand?

2) some ‘kept hands’ are marked as of different rank, although it appears to me that they would have the same expected results.
For instance, 8-J-Q (flush) is labeled higher than 9-J-K. Both are ‘closed’ straights with two JoB cards, none an ace. Why the difference?
Other examples: JK is placed higher than QK ; or 6-8-9 flush higher than 6-7-9. Why?
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beachbumbabs
Joined: May 21, 2013
• Posts: 14227
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September 1st, 2019 at 3:39:19 PM permalink
Quote: kubikulann

Video Poker is not popular here in Brussels. One reason is, the best paytable available is .9687EV (3.13% HE).

For mathematical pleasure, I studied the Wizard’s strategy table.
https://wizardofodds.com/games/video-poker/strategy/a-1-b-37-c-1-d-0-d-1-d-2-d-3-d-4-d-5-d-6-d-25-d-40-d-80-d-50-d-800/

Two things intrigue me.
1) why is it that the strategy does not take into account which cards are discarded? Does it mean that the VP machine draws replacement cards from the whole deck - not restricted to the cards not drawn in the first hand?

2) some ‘kept hands’ are marked as of different rank, although it appears to me that they would have the same expected results.
For instance, 8-J-Q (flush) is labeled higher than 9-J-K. Both are ‘closed’ straights with two JoB cards, none an ace. Why the difference?
Other examples: JK is placed higher than QK ; or 6-8-9 flush higher than 6-7-9. Why?

1) VP is REQUIRED to emulate a standard 52 card deck here, so no, discards are not put back into the deck in a properly designed game, and I don't know what indication you see in the Wizard's strategy page that would make that a question.

2.) I can't answer those, but chances are it has some very small difference, like 1 extra penalty card possible in the lower ranked hold. Those differences are going to be in the thousandth of a percent or even lower.
If the House lost every hand, they wouldn't deal the game.
kubikulann
Joined: Jun 28, 2011
• Posts: 905
September 1st, 2019 at 5:30:11 PM permalink
Quote: beachbumbabs

1) VP is REQUIRED to emulate a standard 52 card deck here, so no, discards are not put back into the deck in a properly designed game, and I don't know what indication you see in the Wizard's strategy page that would make that a question.

When I hold three cards for a straight, for instance, one of the possibilities of win is to make a pair with the two new cards. If one of the discards was a Jack or better, it reduces the chances of that outcome.

Quote: beachbumbabs

2.) I can't answer those, but chances are it has some very small difference, like 1 extra penalty card possible in the lower ranked hold. Those differences are going to be in the thousandth of a percent or even lower.

What is a ‘penalty card’ ?
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bobbartop
Joined: Mar 15, 2016
• Posts: 2542
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September 1st, 2019 at 6:48:14 PM permalink
Quote: kubikulann

What is a ‘penalty card’ ?

Ac Kh Qs Js 4s

Ac Kh Qs Js 4d

The first hand draws to the AKQJ. The 4 of spades is a penalty card to the QJ of spades.

The second hand has no penalty card. Draw to the QJ.

(9-6 Jacks-or-Better)
'Emergencies' have always been the pretext on which the safeguards of individual liberty have been eroded.
DogHand
Joined: Sep 24, 2011
• Posts: 377
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September 1st, 2019 at 11:26:10 PM permalink
Quote: kubikulann

<snip>2) some ‘kept hands’ are marked as of different rank, although it appears to me that they would have the same expected results.
For instance, 8-J-Q (flush) is labeled higher than 9-J-K. Both are ‘closed’ straights with two JoB cards, none an ace. Why the difference?
Other examples: JK is placed higher than QK ; or 6-8-9 flush higher than 6-7-9. Why?

kubikulann,

To understand why 8-J-Q (flush) is labeled higher than 9-J-K in the strategy rankings, look carefully at the intervening line (or lines).

Here is the relevant portion of the WoO's strategy for your game:

3 to a Straight Flush 8JQ; 9JQ
4 to a Straight 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; JQKA
3 to a Straight Flush 89J; 8TJ; 9TJ; 9TQ; 9JK; 9QK

The only entry on the intervening line that applies is the unsuited JQKA. Thus, the strategy is telling you that suited 8JQ (and 9JQ) is higher EV than unsuited JQKA, which in turn is higher EV than suited 9JK and 9QK.

Now assume you're dealt 9h, Jh, Qh, Kc, As. Using the strategy, the best hold is 9h, Jh, Qh.

If instead you're dealt 9h, Jh, Qc, Kh, As, the strategy gives the best hold as Jh, Qc, Kh, As.

Hope this helps!

Dog Hand
kubikulann
Joined: Jun 28, 2011
• Posts: 905
September 2nd, 2019 at 12:02:08 AM permalink
Thank you all!
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kubikulann
Joined: Jun 28, 2011
• Posts: 905
September 2nd, 2019 at 1:59:36 AM permalink
Quote: bobbartop

Ac Kh Qs Js 4s

Ac Kh Qs Js 4d

The first hand draws to the AKQJ. The 4 of spades is a penalty card to the QJ of spades.

The second hand has no penalty card. Draw to the QJ.

So this example confirms that the nature of discards can influence the strategy choice?
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kubikulann
Joined: Jun 28, 2011
• Posts: 905
September 2nd, 2019 at 2:21:45 AM permalink
Quote: DogHand

kubikulann,

To understand why 8-J-Q (flush) is labeled higher than 9-J-K in the strategy rankings, look carefully at the intervening line (or lines).

Here is the relevant portion of the WoO's strategy for your game:

3 to a Straight Flush 8JQ; 9JQ
4 to a Straight 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; JQKA
3 to a Straight Flush 89J; 8TJ; 9TJ; 9TQ; 9JK; 9QK

The only entry on the intervening line that applies is the unsuited JQKA. Thus, the strategy is telling you that suited 8JQ (and 9JQ) is higher EV than unsuited JQKA, which in turn is higher EV than suited 9JK and 9QK.

Now assume you're dealt 9h, Jh, Qh, Kc, As. Using the strategy, the best hold is 9h, Jh, Qh.

If instead you're dealt 9h, Jh, Qc, Kh, As, the strategy gives the best hold as Jh, Qc, Kh, As.

Hope this helps!

Dog Hand

In your example, the difference between 9JQ and 9JK is that the former is ‘open’ and the latter ‘closed’: the former can form a straight 8-Q or a 9-K, while the latter is limited to the second one.
But between 8JQ and 9JK there is no such distinction. Both are closed.

Why in 8h,Jh,Qh,Kc,Ac is playing 8JQ flush better than JQKA unsuited
while in 9h,Jh,Qc,Kh,Ac to play 9JK flush is less than JQKA unsuited ?
I can see that discarding the Qc lowers the chances of getting a straight (which is not the case in 8JQ), but this points to the necessity of looking at discards.

If I understand correctly, the table is not representing EV’s (which depend on discards) but simply priorities in practical choice situations ?
Hmm... let me study that further.
Thanks.
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beachbumbabs
Joined: May 21, 2013
• Posts: 14227
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September 2nd, 2019 at 4:24:18 AM permalink
Quote: kubikulann

In your example, the difference between 9JQ and 9JK is that the former is ‘open’ and the latter ‘closed’: the former can form a straight 8-Q or a 9-K, while the latter is limited to the second one.
But between 8JQ and 9JK there is no such distinction. Both are closed.

Why in 8h,Jh,Qh,Kc,Ac is playing 8JQ flush better than JQKA unsuited
while in 9h,Jh,Qc,Kh,Ac to play 9JK flush is less than JQKA unsuited ?
I can see that discarding the Qc lowers the chances of getting a straight (which is not the case in 8JQ), but this points to the necessity of looking at discards.

If I understand correctly, the table is not representing EV’s (which depend on discards) but simply priorities in practical choice situations ?
Hmm... let me study that further.
Thanks.

"...priorities in practical choice situations. .." is exactly right. That's what the strategy breaks down for you. All possible draws have been calculated, and priorities listed. You simply go from top to bottom.

Some of the choices are so close that a 1-unit difference somewhere in the paytable can change the strategy significantly. That's why, before you learn a strategy, you want to look at the actual machine you will be playing and write down the paytable.

You then go to a strategy calculator (WoO has a good one) and input the game and paytable you'll actually play, and let it generate the info you need.

The particular game at the page you linked is called "6/5 Bonus Poker". That's because the Full House pays 6, and the Flush 5: and the pays for different 4OAK correspond to the Bonus Poker variant (Aces 80:1, 2-3-4 40:1, 5-K 25:1). There are other paytables (such as 7/5 or 8/5) for Bonus Poker, and dozens of other variants of poker (such as Double Bonus, Double Double Bonus, Bonus Deluxe, Triple Double Bonus). Just those few I've listed, with those variables, represent 15 distinct strategies (3 FH unit pays x 5 different 4OAK pays).

Edit: confirming that yes, the cards you discard are very much considered in strategy choices, because you can't receive those cards again. In bobbartop example, discarding the 4s means that if you held the QJs, there would only be 10 remaining spades that could be drawn instead of 11.

When calculating that a flush will pay 5 and a straight 4, and all possible draws, whether that 11th spade is available is the deciding factor on whether to hold 2 to a royal or 4 to an inside straight. So the 4s becomes a penalty card because optimal strategy is not to hold for a RF, and instead try for (and settle for) a lower pay of a straight. That calculation would also include you now have 4 cards that will pay a JOB pair rather than just 2. The value is better with the AKQJ hold.
If the House lost every hand, they wouldn't deal the game.