Dice Probabilities Odds - Willing to Pay

Hi Everyone

I am designing an Asian game of Liar's Dice, I am willing to pay 2 people for this task 250 USDT each (independently)
I want to make sure the odds are correct. Need someone who is good at maths, has a degree and/or knowledge on probabilities.


The rules are as follows:

/document/d/1lSshL_cRbI6Oea3_YfOHtiGGAMq5bqyKXK03Qx3sQxY/edit?tab=t.0


Simplified Version of Liar’s Dice


Dice Rules

A dice has 6 faces with the possible numbers 1, 2, 3, 4, 5, 6 on each face
The number 1 is a 1 AND a wild card, meaning it can also be any other substitute
A dice roll has 5 dices, so eg if a player rolls, and it ends up being 1, 1, 2, 5, 5, this means there are:
2x 1s
2x 3s
2x 4s
2x 6s
3x 2s
4x 5s

The order of the dice face does not matter.


Game Rules

1 Human Player (HP) vs 1 or 2 or 3 other AI/CPU players, the HP can choose the number. Max total 4 players.
Each player rolls 5 dices, the player’s can only see their own dice.
The HP makes a call based on only seeing his own dice.
Once the call is made, all dices are revealed, if the call is within the total dice then the HP wins a pre-set multiplier.


Within the Total

Say for example the HP chooses 1 AI/CPU meaning there are 2 players in total.
HP rolls: 1, 2, 3, 3, 6. The HP can see this information.
CPU/AI 1 rolls: 1, 1, 4, 5, 6. The HP cannot see this information.
Lets say the HP calls 4x 3s, all the dice is then revealed and he wins because the total of the 2 dice are:

3x 1s
4x 2s
4x 4s
4x 5s
5x 3s
5x 6s

There are in fact 5x 3s while the HP called 4x 3s, the HP therefore wins because his call is equal to or smaller than the total of the dice.


Other Points

The HP has the option to call ZAI which means 1s are no longer a wildcard.
So in the above example, if the HP called 4x 3s ZAI he will actually lose because there are only 2x 3s (since the 1 is no longer a wildcard)


The Task

I would like a google sheet table with all the possible combinations of:
The HP’s own hand; and
All the possible 2 player, 3 player, 4 player calls that the HP can make (including ZAI); along with
The probability or odds for each call BASED on the HP's own dice value.

I would need this in a nicely formatted Google sheet so that developer can implement this for a game that I am designing.


Thanks

fanfan,

Perhaps I am missing some subtlety in the rules, but can't the Human Player (HP) guarantee a win on every turn?

Let's use your example: HP rolls: 1, 2, 3, 3, 6.

Can't the HP simply call 3x 3s and thus win, since (counting the 1 is a wild card) he already has three 3's?

Dog Hand

Yeah technically he can but we won't let him call things that are 100% and 0% probability.

We will limit that by application / user interface.

I'm going to just apply a 3% edge to the fair value odds for players to call.

Hope you understand what I mean, those probability of 100% and 0% i will make it that they cannot make such a call.