Liar’s Dice Expected Values


Hello I’m a big dumb idiot and I need some help.

I’ve been trying to wrap my brain around the concept of expected values, specifically for Liar’s Dice. On [Wikipedia]( they have a useful example, saying:

>”Because each rolled die is independent of all others, any combination of values is possible, but the “expected quantity” has a greater than 50% chance of being correct, and the highest probability of being exactly correct. For example, when 15 dice are in play and wilds are used, the expected quantity is 5. The chances of a bid of 5 being correct are about 59.5%; in contrast, the chances of a bid of 8 being correct are only about 8.8%.”

Problem is, I want to figure it out for 10 dice. And the equations and formulas I’ve been finding online to figure that out confuse the hell out of me on account of my being a big stupid idiot. [This was the most useful so far]( but it loses me about halfway through.

Can anyone help? Thanks.

In: Mathematics

Hey. The real number to think about is 3 dice (or 1 in every 3 dice) when using 1 as a wild. Or 6 with no wild, but let’s stick to the 3.
The reason I say 3 is that if you roll 6 dice and they all land on something different, then you have 1 and your desired number, so 2 in 6. 2/6 can be reduced to 1 in 3. These are just odds of course, no actual guarantee. That is why they say the chances of that estimate being correct is 59.5%. So that applies to 1 in 3, 2 in 6, 3 in 9, 4 in 12 and the 5 in 15 you had an example of.
You can use that as a guide so that if there is a dice count in between like 10, you know that there is better than 60% chance of 3, but much less than 60% chance of 4.
All that being said, always take your dice out of the equation when making the guess and add yours after since you know their value. So if there are 10 dice left but 2 are yours, make your estimate based on 8 and then add yours since those are fixed numbers that you can see.
Hope that helps.

Edit, remember to keep it simple because half the fun of this game is having a good poker face and bluffing skills