## Poll

 More than 23,081 hands 4 votes (44.44%) 23,081 hands 2 votes (22.22%) Less than 23,081 hands 3 votes (33.33%)

9 members have voted

ChesterDog
Joined: Jul 26, 2010
• Posts: 922
Thanks for this post from:
April 27th, 2020 at 9:10:41 PM permalink
Quote: smoothgrh

I have been keeping the J.

Regarding 5h 10c Js Qd Kh in 9-6 Jacks or Better, the Wizard's hand analyzer gives these returns:

0.456121 jack
0.293337 ten

https://wizardofodds.com/games/video-poker/hand-analyzer/
gordonm888
Joined: Feb 18, 2015
• Posts: 2730
Thanks for this post from:
April 28th, 2020 at 12:34:39 PM permalink
Royal Flush After 2 Draws with Royal Seeker Strategy

Imagine you find a video poker machine that has a paytable with only one line:

Royal Flush___ 3000

and it says that you may draw twice. That is, you get an initial deal, discard cards, and draw. Then discard cards a second time, and draw a second time. What is the house edge on this unusual video poker game?

Well, I've performed a calculation of the combinations and probabilities associated with that, assuming the player uses a perfect Royal Seeker strategy.

To use an example, on the initial deal let's assume that the player gets two cards that are 10 or higher: a Jack of hearts and a Ten of spades. Now let's assume, the player holds the Jack of hearts, discards the four other cards including the 10 of spades, and draws 4 cards and gets 'AdKd + two other cards that are less than 10.' The calculation assumes that the player will then draw 3 cards to the AdKd on the second draw. If however, on that first draw, the player gets Ace of spades and King of spades, my calculation understands that the spades suit was 'killed' by discarding the 10 of spades on the first draw, and so continues to draw to the Jack of hearts.

Results

After the initial deal, you will have a Royal Flush with a probability of 1.539 E-06, or 1 in 649,740 (approx).
After the first draw, you will have a Royal Flush with a probability of 0.0000433326, or 1 in 23,080.7 (approx).

And, after the 2nd draw, you will have a Royal Flush with a probability of 0.0003326, or 1 in 3,006.375 (approx).

You can see that the 1st draw increases the likelihood of having a Royal Flush by about 28.15X. However the 2nd draw only increases the likelihood of a Royal Flush by a factor of 7.677X.

The first draw involves drawing an average of 3.804 cards; on the 2nd draw an average of 3.364 cards are drawn.

Outcome
Payout
Probability
Return
Royal Flush
3,000
0.000332626
0.997879436
Lose
-1
0.999667374
-0.999667374
Total
1
-0.001787938

So the house edge on this unusual double-draw Royal Flush-only VP game would be about 0.179%.
Last edited by: gordonm888 on Apr 28, 2020
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
tringlomane
Joined: Aug 25, 2012
• Posts: 6267
April 29th, 2020 at 6:47:27 AM permalink
Quote: gordonm888

Royal Flush After 2 Draws with Royal Seeker Strategy

Imagine you find a video poker machine that has a paytable with only one line:

Royal Flush___ 3000

and it says that you may draw twice. That is, you get an initial deal, discard cards, and draw. Then discard cards a second time, and draw a second time. What is the house edge on this unusual video poker game?

Well, I've performed a calculation of the combinations and probabilities associated with that, assuming the player uses a perfect Royal Seeker strategy.

To use an example, on the initial deal let's assume that the player gets two cards that are 10 or higher: a Jack of hearts and a Ten of spades. Now let's assume, the player holds the Jack of hearts, discards the four other cards including the 10 of spades, and draws 4 cards and gets 'AdKd + two other cards that are less than 10.' The calculation assumes that the player will then draw 3 cards to the AdKd on the second draw. If however, on that first draw, the player gets Ace of spades and King of spades, my calculation understands that the spades suit was 'killed' by discarding the 10 of spades on the first draw, and so continues to draw to the Jack of hearts.

Results

After the initial deal, you will have a Royal Flush with a probability of 1.539 E-06, or 1 in 649,740 (approx).
After the first draw, you will have a Royal Flush with a probability of 0.0000433326, or 1 in 23,080.7 (approx).

And, after the 2nd draw, you will have a Royal Flush with a probability of 0.0003326, or 1 in 3,006.375 (approx).

You can see that the 1st draw increases the likelihood of having a Royal Flush by about 28.15X. However the 2nd draw only increases the likelihood of a Royal Flush by a factor of 7.677X.

The first draw involves drawing an average of 3.804 cards; on the 2nd draw an average of 3.364 cards are drawn.

Outcome
Payout
Probability
Return
Royal Flush
3,000
0.000332626
0.997879436
Lose
-1
0.999667374
-0.999667374
Total
1
-0.001787938

So the house edge on this unusual double-draw Royal Flush-only VP game would be about 0.179%.

Very interesting, no way I would have thought a 3000 coin payout would be close to 100% return in a game like this.

But in every VP game I'm aware of, prizes are paid out on a "for 1" basis. So if a game like this pays 3000 for a royal flush, it's really 3000 for 1, or 2999 to 1. And a losing hand is 0 for 1 or -1 to 1. Your chart actually shows the payout for 3000 to 1 basis.

So for the "for one" basis the loss column should be 0 instead and the royal flush at 3000 for 1 would return 0.997879436 to the game, yielding a "house edge" of about 0.212%.
smoothgrh
Joined: Oct 26, 2011
• Posts: 684
May 1st, 2020 at 11:58:15 AM permalink
After 1,000 hands:
Started with \$400
Playing 5x\$0.10
Now at \$132.50
314 wins/1000 hands (31.4%)
46.5% payback

Drew four to a royal on one hand.
Missed holding the ten with a high card about three times early on, but now keeping watch for that.
Am thinking “what have I gotten myself into?”
The prospect of possibly doing this 22 more times (or more) makes me think of the name: Sisyphus.
smoothgrh
Joined: Oct 26, 2011
• Posts: 684
May 13th, 2020 at 3:05:31 PM permalink
I’m theoretically at 10% toward my quest.

2,308 games played
723 games won
31.32% win
5x\$0.10=\$0.50/play
\$1154 played
\$535.50 won
46.40% yield (“payback %”)
Lost \$618.50

Highlights:
One 4-to-a-Royal after the draw.
One quads drawn after one card held.
Approximately 230 minutes of my life that could have been spent doing something else. But it’s all in the name of science and entertainment!
smoothgrh
Joined: Oct 26, 2011
• Posts: 684
July 22nd, 2020 at 5:03:38 PM permalink
Update: I'm at 20% of the 23,081 hands that take on average to get a royal flush using the "Royal or Nothing" strategy. I have not gotten a royal flush.

A few statistics/observations:
—1,425 “winning” hands of 4,700 total hands—about 30.3%
— Payback percentage of 44.76%
— Three “true” 4 to a royal hands, either on the draw, or with drawn cards—the last card not completing the royal
— Three “fake” 4 to a royal hands, in which I finished 4 to a royal, but a non-royal card was drawn before the final card.
— At some point, I felt like this was a “joyless” way to play, wherein the only excitement was to get an occasional full house (I got quads once).
— But later, I realized that even being able to do something as inane as this experiment in my home was a blessing that many others don’t have the time/means/health to do.
— I still think it’s stupid, but it takes only about 10 minutes to play 100 hands, and it’s something I do during my morning coffee or to wind down the day.
tringlomane
Joined: Aug 25, 2012
• Posts: 6267
July 22nd, 2020 at 6:07:32 PM permalink
This is devotion, sir.
DRich
Joined: Jul 6, 2012
• Posts: 6841
July 22nd, 2020 at 6:15:28 PM permalink
Quote: smoothgrh

Update: I'm at 20% of the 23,081 hands that take on average to get a royal flush using the "Royal or Nothing" strategy. I have not gotten a royal flush.

A few statistics/observations:
—1,425 “winning” hands of 4,700 total hands—about 30.3%
— Payback percentage of 44.76%
— Three “true” 4 to a royal hands, either on the draw, or with drawn cards—the last card not completing the royal
— Three “fake” 4 to a royal hands, in which I finished 4 to a royal, but a non-royal card was drawn before the final card.
— At some point, I felt like this was a “joyless” way to play, wherein the only excitement was to get an occasional full house (I got quads once).
— But later, I realized that even being able to do something as inane as this experiment in my home was a blessing that many others don’t have the time/means/health to do.
— I still think it’s stupid, but it takes only about 10 minutes to play 100 hands, and it’s something I do during my morning coffee or to wind down the day.

44% return sounds high if this is a true royal at all costs strategy.
Living longer does not always infer +EV
tringlomane
Joined: Aug 25, 2012
• Posts: 6267
July 25th, 2020 at 6:16:08 AM permalink
Quote: DRich

44% return sounds high if this is a true royal at all costs strategy.

Click on the link in the OP, you'll see it's 48.02% for 9/6 Jacks. He's about right on pace for NOT hitting a royal.

You back into Jacks, 2 pair, and trips: 22.85%, 4.64%, and 2.04% of the time respectively. That adds up. The bigger categories other than quads and SF give back more than 1% return each.
FleaStiff
Joined: Oct 19, 2009