My math-minded brother has some additional thoughts to add to the Liar’s Dice Strategy. I’ve asked him to guest blog about them.

If you want to get nerdy you can add the following when calculating a bid:

Most players use probability when they play: the number and 1’s = 2 options out of six = 1/3 on average for any number. This would suggest if there are 15 dice in play, there should be around 5 of each number.

What some people don’t take into account accurately is their own dice that they already know. With this knowledge, you can use conditional probabilities to calculate a “riskier” bid while still being relatively safe. Essentially, you use the information you already have to calculate how many potential dice there are.

Say there are 3 players, 5 dice each (15 total) anyone should feel pretty safe calling 4 or 5 of any number. However, you know 5 of the dice already, so you should adjust your math! You only don’t know 10 dice, so use the 1/3 estimate on those dice and add in your own. If you have 4 sixes (combination of 1’s and 6’s), then estimate 2-4 sixes under the other players’ cups and add your own 4. That way you can pretty safely bid 6-8 sixes (I’d probably go 7 myself to be a tiny bit safer), which seems like half of the dice.

When someone does the math quickly, 7/15 ~ 50%, a red flag goes off in their brain. They will likely call Dudo. With your 4, it isn’t too hard to get the 7 you need, since each player will likely have 1-2.

Sometimes, you have to take the defensive. Listen to what other players are bidding. If they’re only bidding fives, and all you have is sixes, this may be a good round to take it to ones. Or, use your knowledge of the 5 dice you know (0 fives), and estimate based on the other players’ bids. There can’t be more than 10 fives if you don’t have any, and there are probably more like 7 if they both seem really confident.

This method isn’t foolproof, due to variability and other people having knowledge of their own dice, but you can get the people around you to lose a lot more dice, or at least make them really uncomfortable raising the number, which is where the real fun comes into play.

Be aware, when you are calling your bids, that there is more variability the fewer dice there are (which is how probabilities work: small N, larger variability), so if your dad says “Oh man! Holy moley!” and starts giggling, you should probably just guess he has at least 4 of whatever he’s laughing about and go from there.

Thanks Nathan, great tips.