MattUK
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July 18th, 2020 at 7:46:32 PM permalink
Roxor Gaming has released a Nice Dice game. it's played with 5 dice and three rolls to get the best possible hand. The RTP is 99.54%, so I strongly believe they tried to make an alternative to Craps. The game is available in online casinos owned by Gamesys Group. Below is a link to demo version on VirginGames.
https://www.virgingames.com/?game-info=play-nice-dice
https://www.virgingames.com/game/play-nice-dice/demo
There was already an attempt to find the best strategy, by a Japanese guy here.
https://www.a-taichi.com/tablegame/nicedice.html
I was wondering if the community is up for the challenge.

GAME INFORMATION

The main aim of this game is to roll a scoring hand after three rolls of five dice.
You will have three rolls, with two rounds of holding your dice in-between.
You can choose to hold or not hold as many or as few of the five dice as you wish between rolls.
After the third roll, the game automatically resolves the final configuration of the five dice.

RESULT DESCRIPTION PAYS
Full House *** Three dice of the same value with two other dice of the same value *** Push
Straight *** Five consecutive valued dice *** 1:1
Four of a Kind *** Four dice of the same value and one other non-matching dice *** 3:2
Five of a Kind *** Five dice of the same value *** 3:1
Nice Dice *** Five of a kind on the first roll *** 9:1
Last edited by: MattUK on Jul 19, 2020
ksdjdj
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July 19th, 2020 at 3:33:14 AM permalink
Quote: MattUK

(snip)The RTP is 99.54%, so I strongly believe they tried to make an alternative to Craps. (snip)


Maybe, but it seems closer to a "Yahtzee-like" game to me.

Also, in your post there is a description/copy paste error where it says, "Straight *** Three dice of the same value with two other dice of the same value *** 1:1" as it should be describing a "straight" (e.g. 1-2-3-4-5) but it is just repeating the definition of a "full house"

Here are some links that may be helpful/interesting:

https://en.wikipedia.org/wiki/Yahtzee

https://math.stackexchange.com/questions/320889/yahtzee-large-straight-strategy

http://datagenetics.com/blog/january42012/index.html#:~:text=Finally%2C%20there%20is%20a%2010,or%20the%20second%20one%20does).

---
Spelling not checked thoroughly
MattUK
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July 19th, 2020 at 3:50:18 AM permalink
You're right on both. Nice Dice can be described as simplified Yahtzee and Straight is 1 to 5 or 2 to 6.
Playing it for a while on demo helps to feel the best choices intuitively so I would recommend it. The link is in the first post.
Last edited by: MattUK on Jul 19, 2020
ThatDonGuy
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July 19th, 2020 at 7:33:07 AM permalink
Quote: MattUK

There was already an attempt to find the best strategy, by a Japanese guy here.
https://www.a-taichi.com/tablegame/nicedice.html
I was wondering if the community is up for the challenge.


Sounds easy enough, but I can't find the demo, so I have one question: if I hold (i.e. not reroll) a die for the second roll, can I then choose to reroll it in the third roll?
MattUK
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July 19th, 2020 at 7:48:51 AM permalink
You can choose to stand and the result will be binding. It's a wasted opportunity as long as the hand can be improved.
There is now a link to the demo version in the first post.

I suspect that - much like always going to war with ties in War - player should always try to create Five of a kind. The optimal strategy table may look like this, but this is probably an oversimplification.


Initial roll First decision Second decision
any instant winning hand except Four of a kind stand ---
Four of a kind roll not matching die roll not matching die or stand if matched
1-3-4-5-6 or 1-2-3-4-6 Roll 1 or 6 Roll 1 or 6 if not matched, otherwise stand
2-3-4-5 and one dublet Roll doubled die Roll doubled die if still not Straight, otherwise stand
Three of a kind Roll not matching 2 dice Roll not matching 2 or 1 dice, stand with Five of a kind
One pair Roll not matching 3 dice Roll not matching 3, 2 or 1 dice, stand with Five of a kind
Last edited by: MattUK on Jul 19, 2020
charliepatrick
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July 19th, 2020 at 8:15:07 AM permalink
I'm assuming (using poker dice as it's easier to think it through) if you say held KK and drew QJT then I think you would now go for the outside straight holding KQJT.
ThatDonGuy
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July 19th, 2020 at 9:24:48 AM permalink
The strategy after the second roll is:
Don't break up a full house, three of a kind, or two pair
Keep four to a straight even if it means breaking up a pair; otherwise, hold onto the pair
(i.e. hold onto a pair if the roll includes a 1 and a 6)

As ax example, suppose that, after your second roll, you have 1 1 2 2 6
If you hold the two pair, you have 1/3 chance of a full house (EV 0) and 2/3 of a loss (EV -1), for a total EV of -2/3
If you hold, say, the 1s, then, of the 216 rolls:
1 is 1,1,1 (EV +3)
15 are 1,1,x (EV +1.5)
15 are 1,x,x (EV 0)
5 are a different three of a kind (EV 0)
The other 190 are losing rolls (EV -1)
The total EV is (3 + 22.5 - 190) / 216 = about -0.7616
charliepatrick
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July 19th, 2020 at 9:35:18 AM permalink
Not sure if I've got it totally correct as I get 99.73% (and you can throw away something you held, otherwise it's about 98.9%).

Play as seems obvious except
1st Round
- Full House, only keep Trips.
- Two pairs, keep one pair (K Q J or T if possible) - If you only keep the highest pair it's 99.68%.
- Pair, play the pair unless there's an easy straight draw (e.g. KKQJT).
- Nothing, go for the straight.

2nd Round
- Stand on Full House (it's a shame they've not quite made this an optional play where the EV is the same whether you stand or draw)
- Go for any straight draw (i.e. discard from the pair)
- Draw one card to Two Pairs.

Note: Sorry I didn't make it clear that I was using Poker Dice (easier to think), so for K Q J T read 5 4 3 2 and KKQJT read 55432. With Two Pairs on the 1st round, if you have a choice throw away the 11 or 66.
Last edited by: charliepatrick on Jul 19, 2020
MattUK
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July 19th, 2020 at 9:44:57 AM permalink
Quote: ThatDonGuy

The strategy after the second roll is:



You can't talk about the second decision without resolving the first one (what to do in all cases). Probably that's why you have that funny 23.84% RTP. It's like American Roulette with 29 zeros. Please consider looking on that Japanese website and translate using Google.
https://www.a-taichi.com/tablegame/nicedice.html
It's not easy to go through his tables, but he did it Wizard-style. Ideally, we should also have EV for any case to be able to compare them and see the increase (unless it was a risk worth taking, but the roll decreases the EV, which in principle may happen).
Here is his summary. I am trying to figure out what the oriental names describe.
https://drive.google.com/file/d/1lk10B2ZT5NfidfwgKf-ZDxDXPlTEGZdS/view?usp=sharing
Last edited by: MattUK on Jul 19, 2020
MattUK
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July 19th, 2020 at 9:50:11 AM permalink
Quote: charliepatrick


- Two pairs, keep one pair (K Q J or T if possible) - If you only keep the highest pair it's 99.68%.
- Pair, play the pair unless there's an easy straight draw (e.g. KKQJT).
- Draw one card to Two Pairs.



Ehm... Charlie... it's a wrong thread. This one is about a dice game. :-)
charliepatrick
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July 19th, 2020 at 9:58:20 AM permalink
Quote: MattUK

Quote: charliepatrick


- Two pairs, keep one pair (K Q J or T if possible) - If you only keep the highest pair it's 99.68%.
- Pair, play the pair unless there's an easy straight draw (e.g. KKQJT).
- Draw one card to Two Pairs.



Ehm... Charlie... it's a wrong thread. This one is about a dice game. :-)

Possibly you missed my earier comment that I was going to use poker dice as it makes it easier to think about Straights etc. So it was easier for me to see that "KQJT" is an outside straight draw than "5432". Sorry if that caused confusion.
ThatDonGuy
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July 19th, 2020 at 10:41:22 AM permalink
Quote: MattUK

You can't talk about the second decision without resolving the first one (what to do in all cases). Probably that's why you have that funny 23.84% RTP. It's like American Roulette with 29 zeros. Please consider looking on that Japanese website and translate using Google.
https://www.a-taichi.com/tablegame/nicedice.html
It's not easy to go through his tables, but he did it Wizard-style. Ideally, we should also have EV for any case to be able to compare them and see the increase (unless it was a risk worth taking, but the roll decreases the EV, which in principle may happen).
Here is his summary. I am trying to figure out what the oriental names describe.
https://drive.google.com/file/d/1lk10B2ZT5NfidfwgKf-ZDxDXPlTEGZdS/view?usp=sharing


Here's the first roll strategy:
Five Of A Kind - hold all five
Four Of A Kind - hold the four; reroll the other die
Straight - hold all five
Full House - hold all five
Three Of A Kind - hold the three; reroll the other two dice
Two Pair - hold one of the pair; reroll the other three dice
2345 and a Pair - keep 2345, and break up the pair
One Pair (other than with 2345) - hold the pair, and reroll the other three
12346, 12356, 12456, 13456 - reroll the 1 and the 6, and keep the other three

The RTP is 99.5376324%


Here's the complete strategy:

Five Of A Kind - hold all five

Four Of A Kind - hold the four; reroll the other die

Straight - hold all five

Full House - hold all five

Three Of A Kind - hold the three; reroll the other two dice

Two Pair
First roll: hold one of the pair; reroll the other three dice
Second roll: hold both pairs; reroll the other die

One Pair
First roll: if you have 2345, keep the 2345, and break up the pair; otherwise, hold the pair, and reroll the other three
Second roll: if you have a 1 and a 6, hold the pair, and reroll the other three; otherwise, keep the 4 to a straight (even an inside straight), and break up the pair

12346, 12356, 12456, 13456
First roll: reroll the 1 and the 6, and keep the other three
Second roll: reroll the 1 (or the 6), and keep the other four
Last edited by: ThatDonGuy on Jul 19, 2020
MattUK
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July 19th, 2020 at 2:08:33 PM permalink
I still think that to mark the job done we should have return values for every case. Can the EV go backward (when the risk is worth taking but backfires)?


Initial roll First decision Second decision
Five of a kind stand stand
Four of a kind reroll unmatched die reroll unmatched die
Straight stand stand
Full House hold Three of a kind, reroll the other two dice stand
Three of a kind reroll the other two dice reroll the other two dice
Two Pair hold inside Pair if you can; reroll the other three dice hold both pairs; reroll the other die
One Pair and 2345 hold the 2345; reroll the paired die hold the 2345; reroll the paired die
One Pair and one Outsider* hold the pair, and reroll the other three hold 4 to a Straight, and reroll the paired die
One Pair and both Outsiders* hold the pair, and reroll the other three hold the pair, and reroll the other three
13456, 12456, 12356, 12346 reroll both Outsiders*, and hold the other three reroll either Outsider*, and hold the other four

* Outsiders are numbers 1 and 6

The above table takes into account subsequent discussion and corrections.
Last edited by: MattUK on Jul 19, 2020
ThatDonGuy
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July 19th, 2020 at 2:38:46 PM permalink
Everything is correct except for the One Pair (and even then, One Pair and 2345 is correct):

Initial roll First decision Second decision
One Pair and 2345 hold the 2345; reroll the paired die hold the 2345; reroll the paired die
One Pair, and either but not both 1 or 6** hold the pair, and reroll the other three hold 4 to a straight, and reroll the paired die
One Pair, and both 1 and 6** hold the pair, and reroll the other three hold the pair, and reroll the other three

** note the 1 and 6 may or may not be in the pair; for example, both 1 2 4 4 5 and 2 3 5 6 6 are "one pair, and either but not both 1 or 6," and both 1 1 2 3 6 and 1 4 4 5 6 are "one pair, and both 1 and 6"
charliepatrick
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July 19th, 2020 at 3:05:08 PM permalink
Apologies for using AKQJT9 rather than 123456 (or 654321). I now agree with the RTP but there's still the need to hold an inside Pair when you choose which Pair to hold from Two Pairs after the first roll. Also note you only keep the Trips after the first roll with a Full House, but you keep the Full House after the second roll.
Initial Roll Outcome
Nice Dice (AAAAA)
6
10.000
Quads (AAAAK)
150
2.958
Straight (AKQJT)
240
2.000
Trips or FH (AAA??)
1 500
1.539
Easy Str Draw (KKQJT)
240
1.111
2 Pair As & 9s (AA99x)
120
0.742
2 Pairs (AAKKx)
1 680
0.755
Pair As or 9s (AAxxx)
1 200
0.742
Pair Ks Qs Js Ts (KKxxx)
2 160
0.755
Inside Straight (AKQJ9)
480
0.634
First Roll
Nice Dice (AAAAA)
10.000
Stand
Fiver (AAAAA)
4.000
Stand
Quads (AAAAK)
2.958
Draw one
Full House (AAAKK)
1.000
(i) Stand
Full House (AAAKK)
1.539
(ii) Keep Trips
Straight (AKQJT)
2.000
Stand
Trips (AAAxx)
1.539
Keep Trips
Pair / E Str (KKQJ T)
0.755
(i) Keep Pair (K Q J or Ts)
Pair / E Str (KKQJ T)
1.111
(ii) Straight Draw
Pair / I Str (AAKQJ)
0.742
(i) Keep Pair (As or 9s)
Pair / I Str (AAKQJ)
0.611
(ii) Straight Draw
Pair / I Str (KKxxx)
0.755
(i) Keep Pair (K Q J or Ts)
Pair / I Str (KKAQJ)
0.611
(ii) Straight Draw
Two Pair (AA99x)
0.742
(i) Keep Pair (As or 9s)
Two Pair (AA99x)
0.556
(ii) Keep Two Pair
Two Pair (KK99x)
0.755
(i) Keep Pair (K Q J or Ts)
Two Pair (KK99x)
0.556
(ii) Keep Two Pair
Pair (As or 9s) (AAxxx)
0.742
(i) Keep Pair (As or 9s)
Pair (Ks Qs Js Ts) (KKxxx)
0.755
(i) Keep Pair (K Q J or Ts)
Inside Str (AKQJ9)
0.611
(i) Keep 4 to Str
Inside Str (AKQJ9)
0.634
(ii) Keep KQJ
Inside Str (AKQT9)
0.611
(i) Keep 4 to Str
Inside Str (AKQT9)
0.634
(ii) Keep KQT
Inside Str (AKJT9)
0.611
(i) Keep 4 to Str
Inside Str (AKJT9)
0.634
(ii) Keep KJT
Inside Str (AQJT9)
0.611
(i) Keep 4 to Str
Inside Str (AQJT9)
0.634
(ii) Keep QJT
Second Roll
Nice Dice (AAAAA)
10.000
Stand
Fiver (AAAAA)
4.000
Stand
Quads (AAAAK)
2.750
Draw one
Full House (AAAKK)
1.000
(i) Stand
Full House (AAAKK)
0.944
(ii) Keep Trips
Straight (AKQJT)
2.000
Stand
Trips (AAAxx)
0.944
Keep Trips
Pair / E Str (KKQJ T)
0.285
(i) Keep Pair
Pair / E Str (KKQJ T)
0.667
(ii) Straight Draw
Pair / I Str (AAKQJ)
0.285
(i) Keep Pair
Pair / I Str (AAKQJ)
0.333
(ii) Straight Draw
Two Pair (AAKKx)
0.285
(i) Keep Pair
Two Pair (AAKKx)
0.333
(ii) Keep Two Pair
Pair (AAxxx)
0.285
Keep Pair
Inside Str (AKQJ9)
0.333
Keep 4 to Str
Return to player
99.537 632%
MattUK
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July 19th, 2020 at 3:39:38 PM permalink
Quote: charliepatrick

I now agree with the RTP but there's still the need to hold an inside Pair when you choose which Pair to hold from Two Pairs after the first roll. Also note you only keep the Trips after the first roll with a Full House, but you keep the Full House after the second roll.


Great! Now we're in agreement with the Japanese guy! He had 10 different outcomes, wrote "Hold one pair in the middle" for the first decision having Two Pair and that it's better to reroll two unmatched dice having Full House.
I am beginning to understand what ThatDonGuy had in mind. Somehow Mr. Toyoda did the same, but that was too fragmented piece of the puzzle to understand without background, sorry.
I corrected the table and added "if you can" because it's still possible to roll 1166 and inside number.
PS: Nice Dice is not formed after a decision. They can be removed from the bottom two return tables. Hope that doesn't change anything.
Last edited by: MattUK on Jul 19, 2020
MattUK
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July 20th, 2020 at 9:19:54 AM permalink
It was laborious, but here is the final answer. My thanks to charliepatrick and thatdonguy for doing the calculations.

"First decision" table


Initial roll First decision Expected value
Five of a kind stand 4.000
Four of a kind reroll unmatched die 2.958
Straight stand 2.000
Three of a kind hold three of a kind, reroll the other two dice 1.539
Full House hold three of a kind, reroll the other two dice 1.539
insider Pair and 2345 hold the 2345, reroll the paired die 1.111
insider Pair and 1 or 6 hold the pair, reroll the other three 0.755
11 or 66 Pair hold the pair, reroll the other three 0.742
Two Pair 11 and 66 hold either pair, reroll the other three 0.742
any other Two Pair hold insider pair, reroll the other three 0.755
13456, 12456, 12356, 12346 reroll 1 and 6, hold three insiders 0.634


"Second decision" table


Second roll Second decision Expected value
Five of a kind stand 4.000
Four of a kind reroll unmatched die 2.750
Straight stand 2.000
Three of a kind reroll the other two dice 0.944
Full House stand 1.000
insider Pair and 2345 hold the 2345, reroll the paired die 0.667
insider Pair and 1 or 6 hold 4 to a Straight, reroll the paired die 0.333
Two Pair 11 and 66 hold both pairs, reroll the other die 0.333
any other Two Pair hold both pairs, reroll the other die 0.333
13456, 12456, 12356, 12346 reroll 1 or 6, hold the other four 0.333
11 or 66 Pair hold the pair, reroll the other three 0.285


Strategy for Two Pairs can be merged into "hold insider Pair if you have it, otherwise either pair; reroll the other three". Likewise, some cells can be merged if EV is ditched.
Note that the EV decrease in the second round for every outcome, except instant winners Five of a kind and Straight.
For the avoidance of doubt, Yahtzee aka Nice Dice returning 10x is an automatic winner after the initial roll and hence cannot be formed.
Just maybe some people would like to have all five columns in a landscape and print out horizontally. It can be done, but not exactly using html.
And finally, here's their "handy video tutorial":
https://www.linkedin.com/posts/roxor-gaming_roxorgaming-wemakeplaymorerewarding-igaming-activity-6689475826964033536-aZk9/
Last edited by: MattUK on Jul 20, 2020
WatchMeWin
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July 20th, 2020 at 9:23:12 AM permalink
I have a feeling this game will have a much greater probability of success in inner city casinos...
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unJon
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July 20th, 2020 at 9:24:18 AM permalink
Quote: MattUK

It was laborious, but here is the final answer. My thanks to charliepatrick and thatdonguy for doing the calculations.

"First decision" table


Initial roll First decision Expected value
Five of a kind stand 4.000
Four of a kind reroll unmatched die 2.958
Straight stand 2.000
Three of a kind reroll the other two dice 1.539
Full House hold Three of a kind, reroll the other two dice 1.539
insider Pair and 2345 hold the 2345, reroll the paired die 1.111
insider Pair and 1 or 6 hold the pair, reroll the other three 0.755
11 or 66 Pair hold the pair, reroll the other three 0.742
Two Pair 11 and 66 hold either pair, reroll the other three 0.742
any other Two Pair hold insider pair, reroll the other three 0.755
13456, 12456, 12356, 12346 reroll 1 and 6, hold three insiders 0.634


"Second decision" table


Second roll Second decision Expected value
Five of a kind stand 4.000
Four of a kind reroll unmatched die 2.750
Straight stand 2.000
Three of a kind reroll the other two dice 0.944
Full House stand 1.000
insider Pair and 2345 hold the 2345, reroll the paired die 0.667
insider Pair and 1 or 6 hold 4 to a Straight, reroll the paired die 0.333
Two Pair 11 and 66 hold both pairs, reroll the other die 0.333
Tany other Two Pair hhold both pairs, reroll the other die 0.333
13456, 12456, 12356, 12346 reroll 1 or 6, hold the other four 0.333
11 or 66 Pair hold the pair, reroll the other three 0.285


The tables can be slightly simplified by giving recommendation "hold insider Pair if you have it, reroll the other three".
Note that the EV decreas in the second round for every outcome, except Five of a kind and Straight.



Nice table. Only commented is EV on first roll for five of a kind. I thought this got the nice dice bonus?
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MattUK
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July 20th, 2020 at 9:33:37 AM permalink
Quote: unJon

Nice table. Only commented is EV on first roll for five of a kind. I thought this got the nice dice bonus?


I skipped that because it does not require a decision, but it's included in the 99.54% RTP.
Wizard
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July 20th, 2020 at 4:47:15 PM permalink
Sorry for the late arrival. I have tried every link in this thread to play a demo, but none seem to have the game or I'm rebuffed by a password request. However, this video was helpful.

Questions:
1. Can I re-roll a die already placed in the tray?
2. If I'm happy with what I have after the first or second roll, must I re-roll? If not, how does the player indicate he doesn't want any remaining rolls?

I would appreciate a nice screen-shot of the game from anybody who has password access.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MattUK
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July 20th, 2020 at 5:47:37 PM permalink
Quote: Wizard

1. Can I re-roll a die already placed in the tray?
2. If I'm happy with what I have after the first or second roll, must I re-roll? If not, how does the player indicate he doesn't want any remaining rolls?

I would appreciate a nice screen-shot of the game from anybody who has password access.



1. The tray is a nice representation of held dice. You can change your mind and un-click them before you press "ROLL".
2. You always can stand - by pressing the "STAND" button. If it's throwing away the stake you will be asked for confirmation as safety net.
3. as per your request - https://drive.google.com/file/d/1JuyoKI8ey54ZQn3zOfNR0Sm1j6ZkZIU7/view?usp=sharing
Wizard
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July 20th, 2020 at 10:04:32 PM permalink
Thank you Matt.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MattUK
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July 21st, 2020 at 4:39:10 AM permalink
Because like every wacko I like doing things to completion, here's the 1-page best strategy ready to print. Two, actually. One most user-friendly, the other with EV. It's in open file format so easy to copy and change. Maybe it's worth releasing urbi et orbi.
https://drive.google.com/file/d/1tQuGA70dPMElB_UH3pAGr9fHayfYY59z/view?usp=sharing
DJTeddyBear
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July 21st, 2020 at 6:37:17 AM permalink
MattUK -
Nice job, but I wish there was also a chart showing the possibility of each hand at the end of 3 rolls. Kind of important when figuring the house edge.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
MattUK
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July 21st, 2020 at 7:36:08 AM permalink
Quote: DJTeddyBear

MattUK -
Nice job, but I wish there was also a chart showing the possibility of each hand at the end of 3 rolls. Kind of important when figuring the house edge.


Sorry to disappoint. :-) The house edge is what it is - 0.46% when making best choices. Just between Pass Line and Don't Pass Line in Playtech Craps. A pity they did not best Don't Pass Line, in my opinion. This game is more complex than Craps so should be 99.60-99.70%. 0.1% from heaven. Alas, still great game, where you need to earn an almost equal chance against the casino.
Last edited by: MattUK on Jul 21, 2020
Wizard
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July 22nd, 2020 at 10:07:22 AM permalink
Quote: MattUK

Because like every wacko I like doing things to completion, here's the 1-page best strategy ready to print. Two, actually. One most user-friendly, the other with EV. It's in open file format so easy to copy and change. Maybe it's worth releasing urbi et orbi.
https://drive.google.com/file/d/1tQuGA70dPMElB_UH3pAGr9fHayfYY59z/view?usp=sharing



Very nice work! May I use this on Wizard of Odds? I'm happy to give proper attribution, of course. Just let me know how you would like to be known.

I am about 80% done with a program to analyze the game and it is looking like it may run rather slowly if the player ever re-rolls four dice. Never a need to re-roll all five, obviously. It seems clear from your strategy that the player never rolls four, but just to be safe, can you confirm that?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MattUK
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July 22nd, 2020 at 10:42:52 AM permalink
Of course you can! That's the plan, actually, and just MattUK will be fine.
I think it's rather clear that
(1) the only way to improve having Four of a kind is to go for Five of a kind,
(2) you must roll, or you'll waste the opportunity to improve from 2.500 to 4.000
(3) it's FAR easier to match the fifth die to the Four of a kind (match the tail to a dog) than four dice to the fifth (match the dog to a tail).
The usefulness of this reasoning is not exhaustive.
DJTeddyBear
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July 22nd, 2020 at 12:15:07 PM permalink
I can稚 think of any reason to save just one die - unless they add something whacky such as six separate progressives for the six different 5OAKs, and your 5 dice are not a straight, AND one (or more) of the progressives is particularly high.

And I bet if the game gets any traction at all, they will add those progressives.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
MattUK
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July 23rd, 2020 at 10:17:56 AM permalink
There are not many casino games with over 99% RTP, which one could play for long with a peace of mind. It's occupied by video poker, all blackjack, Spanish21, Pontoon (both blackjack cousins anyway) and Craps. Playtech has had one slot flirting with that idea - Goblin's Cave with 99.32% RTP if played with max coins. However, without knowing the probabilities of picking up the treasures no one knew the best strategy so it was a tragically wasted opportunity to create something unique. Nice Dice takes off where Goblin's Cave has failed. Anyone can create or check the best strategy and play safely hundreds of rounds as long as the numbers are generated randomly, which is not in question. Nice Dice, er, Job, Roxor Gaming!
Last edited by: MattUK on Jul 23, 2020
Wizard
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July 23rd, 2020 at 12:11:40 PM permalink
Quote: ThatDonGuy

The RTP is 99.5376324%



Not to say this is wrong, but the following table shows what I'm getting. My EV equates to an RTP of 96.7941%. Any thoughts about something I may not be seeing. I've gone over my code over and over, rewriting it, and I always get the same bottom line.

The only thing I can think of is my program never re-rolls 4 or all 5 dice. Your strategy says not to do that anyway. I'm stumped.

Event Pays Combinations Probability Return
Five of a kind on first roll 9 362,797,056 0.000772 0.006944
Five of a kind 3 18,570,954,240 0.039497 0.118491
Four of a kind 1.5 86,360,256,000 0.183673 0.275509
Straight 1 33,457,950,720 0.071159 0.071159
Full house 0 94,383,221,760 0.200736 0.000000
Loser -1 237,049,804,800 0.504163 -0.504163
Total 470,184,984,576 1.000000 -0.032059
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
charliepatrick
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July 23rd, 2020 at 2:03:29 PM permalink
I agree with the paying figures except I get 39 907 676 160 straights, so it looks as if you've lost some after the 1st roll with hands like KKQJT (i.e. Pair and Easy Straight) 622080 and half the no pair straight draws (AKQJ9 etc) (414720/2).
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July 23rd, 2020 at 2:42:31 PM permalink
Quote: charliepatrick

I agree with the paying figures except I get 39 907 676 160 straights, so it looks as if you've lost some after the 1st roll with hands like KKQJT (i.e. Pair and Easy Straight) 622080 and half the no pair straight draws (AKQJ9 etc) (414720/2).



Thanks Charlie. Stupid question -- the video shows the game being played with dice numbered 1 to 6. However, you refer to poker dice (9 to A). This would't make any difference would it? Aces high only, right?

My program just loops and makes the best of the 26 plays that re-roll 0 to 3 dice (never 4 or 5). I coded no strategy decisions in it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
charliepatrick
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July 23rd, 2020 at 3:00:05 PM permalink
When I saw the puzzle I just thought of poker dice and stuck with the idea, I found it easier to visualise AKQJ9 than 65431.

What I originally used was a simple spreadsheet that just looked at EVs and percentages of various options. It looked at the chances of drawing different types of hands given your current set of dice. But it was easy to work out how many combinations this meant at various stages given the strategy. Luckily, unlike poker with cards, there's no memory of the discards since the dice are rerolled.
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July 23rd, 2020 at 4:12:55 PM permalink
Charlie, not to doubt you, but has anyone else verified your number? I have seen MattUK quoting it, but Matt, can you confirm it?

I would like to starting writing a page on the game and thinking about posting both of our figures for now.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MattUK
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July 23rd, 2020 at 4:35:02 PM permalink
Gamesys Group says that the RTP is 99.54%. As you know, the British market is heavily regulated with 7 digits penalties for failing to play by the rules. That's why I have a good deal of confidence that Charlie has verified that independently.

***

RETURN TO PLAYER

Return To Player (RTP): 99.54%

The expected return is the amount we pay out to players relative to the amount of wagering on the game.

For example, if we take £100 of wagers we will, on average, pay out £99.54 of wins. This return is based on the player making the best choices.
CrystalMath
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July 23rd, 2020 at 4:36:50 PM permalink
Quote: Wizard

Charlie, not to doubt you, but has anyone else verified your number? I have seen MattUK quoting it, but Matt, can you confirm it?

I would like to starting writing a page on the game and thinking about posting both of our figures for now.



I get 99.5376324% also.
I heart Crystal Math.
charliepatrick
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July 23rd, 2020 at 4:38:28 PM permalink
It was quoted earlier, but I think if you can agree with my number for straights, you'll get the same figure. I cannot be certain that I have the correct strategy, but it sounds as if your method would have proved it. Personally I'd put the EVs in EV order with a note about splitting a FH on the first round, which pairs to split from Two Pair, and with a pair always going for an outside straight draw and an inside straight draw on the second round etc.
ThatDonGuy
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July 23rd, 2020 at 4:41:15 PM permalink
Quote: CrystalMath

I get 99.5376324% also.


As did I.
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July 23rd, 2020 at 4:44:51 PM permalink
Thanks everyone for the confirmation.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
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July 23rd, 2020 at 5:24:16 PM permalink
I think I have found my error. It was how the program handled a dealt straight on the first roll. It did not properly weight it, so the player was throwing it away.

It takes my program about two hours to cycle. Hope to have good news soon. My EV's on some sample hands agrees with those of MattUK.

Thanks again everybody for your help!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
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July 23rd, 2020 at 6:35:50 PM permalink
Quote: DJTeddyBear

Nice job, but I wish there was also a chart showing the possibility of each hand at the end of 3 rolls. Kind of important when figuring the house edge.


Here's the complete breakdown:

362,797,096 Nice Dice
18,570,954,200 Five of a Kind (except Nice)
86,360,256,000 Four of a Kind
94,383,221,760 Full House
39,907,676,160 Straight
86,556,211,200 Three of a Kind
70,073,579,520 Two Pair
63,892,592,640 One Pair
10,077,696,000 No Pair/Straight (12346, 12356, 12456, 13456)
Wizard
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July 23rd, 2020 at 7:10:36 PM permalink
I found the bug in my program. It effectively didn't let the player keep a pat hand, except a five of a kind, on the first roll. Here are my new numbers.

Event Pays Combinations Probability Return
Five of a kind on first roll 9 362,797,056 0.000772 0.006944
Five of a kind 3 18,570,954,240 0.039497 0.118491
Four of a kind 1.5 86,360,256,000 0.183673 0.275509
Straight 1 39,907,676,160 0.084877 0.084877
Full house 0 94,383,221,760 0.200736 0.000000
Loser -1 230,600,079,360 0.490445 -0.490445
Total 470,184,984,576 1.000000 -0.004624


They could have had a much more attractive pay table if a straight paid more than four of a kind. In the game of Yahtzee, a large straight pays 40, while a four of a kind pays only the "sum of the dice," which would average 17.5 assuming no strategy to go for the higher four-of-a-kinds.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MattUK
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July 23rd, 2020 at 7:51:31 PM permalink
Personally, I like to think that the chance to get Nice Dice is 1/1296 and the return is 9/1296 = 1/144. On your table, it's extended by as much as 6^7. Still true, but devoid of much of elegance. For the same reason, the total number is 6^15 and all values can be divided by at least 6^7 to get more manageable figures.
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July 23rd, 2020 at 8:32:31 PM permalink
Quote: MattUK

Personally, I like to think that the chance to get Nice Dice is 1/1296 and the return is 9/1296 = 1/144. On your table, it's extended by as much as 6^7. Still true, but devoid of much of elegance. For the same reason, the total number is 6^15 and all values can be divided by at least 6^7 to get more manageable figures.



The reason the total is 6^15, is that you have six dice that can be rolled three times. Much like in video poker many of my return tables total to 5*combin(52,5)*combin(47,5), although there is usually a common denominator to each line item.

After all the work I put into my program, I prefer to leave the raw results as they are.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
rsactuary
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July 23rd, 2020 at 8:46:19 PM permalink
Your answers differ than Don Guy's by 40 in the 5 of a kind (not nice) and loser categories.

Not sure who is wrong, but someone is!
Torghatten
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July 23rd, 2020 at 8:49:20 PM permalink
Quote: rsactuary

Your answers differ than Don Guy's by 40 in the 5 of a kind (not nice) and loser categories.

Not sure who is wrong, but someone is!



470,184,984,576 / 1296 shows that Wizard is right.
charliepatrick
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July 24th, 2020 at 3:16:20 AM permalink
I agree with the wizazrd's numbers. You can confirm the Nice Dice as it's 7776*7776*6 (six ways to get the five of a kind, no dice rerolled so all 6^5 combinations, repeat). btw I classified the One Pair events as the strategy was different for them.
EventCombinationsPaysContribution
Nice Dice
362 797 056
10
3 627 970 560
Fiver
18 570 954 240
4
74 283 816 960
Quads
86 360 256 000
3
215 900 640 000
FH
94 383 221 760
1
94 383 221 760
Straight
39 907 676 160
2
79 815 352 320
Trips
86 556 211 200
Two Pair
70 073 579 520
Pair/EasyStr
14 511 882 240
Pair/InStr
40 310 784 000
Pair/NoStr
9 069 926 400
Inside Str
10 077 696 000
TOTAL
470 184 984 576
468 011 001 600
Any Pair
63 892 592 640
RTP:
99.537 632 411%
ThatDonGuy
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July 24th, 2020 at 7:03:15 AM permalink
Quote: rsactuary

Your answers differ than Don Guy's by 40 in the 5 of a kind (not nice) and loser categories.

Not sure who is wrong, but someone is!


My "loser numbers" add up to the Wizard's.

You're right about the "not nice 5 of a Kind" number; I calculated the total 5 of a Kind count and then subtracted the wrong number of Nice Dice rolls. Notice that my Nice Dice number is off by 40 as well.
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July 24th, 2020 at 9:31:53 AM permalink
I have an initial draft of my WoO page on Nice Dice. Please have a look. I reworded the strategy into my own words. If there is anything I got wrong of omitted, please let me know.

Thanks in advance.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
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