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.Quote:MattUKQuote: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. :-)

Quote:MattUKYou 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

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.

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"

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% |

Quote:charliepatrickI 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.

"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/

Quote:MattUKIt 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?

Quote:unJonNice 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.