Dudo Strategy and Odds

Dudo, a Game of Math as Much as Bluff

In Dudo, the dice are down to chance, but your bids are a choice. By counting your own dice and estimating what is hiding under the other cups, you can choose your bids better, spot risky bids and bluff at the right time. These tips also apply to other versions of the game, including commercial editions such as Perudo®. This guide assumes you already know the Dudo rules.

The basic odds

A die has a one-in-six chance of showing a given face. Pacos (the 1s) are wild: each hidden die therefore has a one-in-three chance of counting for the bid value. For Pacos themselves, the probability stays at one in six.

• Average number of dice of a value (Pacos included) among the hidden dice: hidden dice ÷ 3.
• Average number of Pacos among the hidden dice: hidden dice ÷ 6.
• Add your own dice of that value (and your Pacos): you get your estimate of the total on the table.

Table of safe bids

This table shows the probability that the hidden dice contain at least a given number of dice of a specific value (Pacos included). It also helps estimate your chances of a successful Calza.

Key takeaway: if a bid asks the hidden dice for one die more than their average, it already has less than a fifty-fifty chance of being right. With two dice more, it becomes very risky.

Building a good bid

• Start from your own dice: preferably bid a value you hold several of, Pacos included. You are then the best-informed player at the table.
• Stay under your estimate: as long as the bid does not exceed your dice plus the average of the hidden dice, you are on safe ground.
• Think about the next player: a bid just under the estimate puts them in a tough spot, raise or doubt.
• Watch your opponents' bids: a player who raises the quantity without changing the face may have several dice of that value. A change of face can also be a way to restart the bidding.

When to call Dudo?

Subtract from the bid quantity the dice of that value you hold, Pacos included. The rest must be with the other players. If that number exceeds the estimated average by at least one die, the bid has less than a fifty-fifty chance of being right: a Dudo is then worth trying.

Remember that if you are wrong, you are the one who loses a die. When you have few left, prefer a reasonable raise to a tight Dudo.

When to try Calza?

Calza only wins if the count is spot on. With five or more hidden dice, its chances do not exceed one in three, and they drop as the number of dice grows. Save it for bids that match your estimate exactly.

Late in the game, Calza becomes more attractive. If your dice already match the bid quantity exactly and only two hidden dice remain, neither of them must match the bid value for the total to stay exact: the probability is 44%. With a single hidden die, it climbs to 67%. That is a good chance to win a die back.

Playing Pacos well

There are on average half as many Pacos as dice of a given value. The conversion rule (halve the quantity, rounded up) is therefore almost neutral: switching to Pacos is mostly useful to break an escalating bid on a face you do not hold.

Going back to regular faces is costly (double plus one): only bid Pacos if you have some yourself, otherwise the next player will often have no choice but to doubt… you.

The art of bluffing

• Vary your openings: if you always bid your best face, your opponents will eventually read your game.
• The false start: open on a value you don't have, then return to your real strength on the next turn. The others may raise without holding many dice of that value.
• Keep a steady rhythm: online too, a long pause often betrays hesitation.
• Bluff while you still have dice: a failed bluff costs a die. It's better to take the chance when you have five left than when you're down to two.

Playing a palifico round

In palifico, Pacos are no longer wild and the value is fixed by the first bid: each hidden die only has a one-in-six chance of matching. Bids should therefore be more modest. If you open the round with your only die, bid its value: you are the only one who knows there is at least one.

Common mistakes

• Forgetting Pacos in your estimate, or on the contrary counting them in a bid on Pacos.
• Reasoning on the total number of dice instead of only the dice you cannot see.
• Raising out of reflex when a Dudo was statistically a winner.
• Trying a Calza early in the game, when dozens of dice are in play.

The best way to improve is still to play. Start a game of Dudo online, free and without signing up, to put these tips into practice.