There are several similar games that go under the name I Doubt It! or Bullshit. The idea of all these games is that you try to get rid of all your cards by playing them face down according to some rule. If anyone thinks you have broken the rule they can challenge. After a challenge the last play is exposed and whoever was in the wrong has to pick up the played cards.
The version of "I Doubt It" most often found in card game books has each player playing the next rank above or below the previous play. The rules of that version are given on the Bullshit page.
The game described on this page, known as I Doubt It, or IDI for short, players must all (pretend to) play the same rank of card until someone challenges. It is somewhat similar to the Russian game Verish' ne Verish' (Trust - Don't Trust). Although it is a children's game, the strategy is very interesting and can get quite convoluted.
Another, more elaborate game in which the cards are played face down and challenged is the Finnish game Valepaska.
There can be three or more players - probably no more than six. It is possible for two to play, but then the force variation must be played. A standard pack is used, with no jokers. An equal number of cards (five or more) is dealt to each player's hand. Each player must keep the number of cards that they own clearly visible at all times.
The objective is to get rid of all the cards in your hand.
One player, designated as the lead, begins a round by playing a single card face down, starting a stack in the center of the table, and announcing a rank - such as "queen", "seven", "ace", etc. Suit doesn't matter - just rank. The card played may or may not actually match the announced rank, but no one knows for sure except the person who played it.
Going clockwise, each player then takes a turn consisting of one of two options:
The play continues around the table as many times as necessary until everyone passes or there is a challenge. Note that if all the other players pass, it is perfectly legal (and very common) for one player to repeatedly add cards to the stack.
The round can end in two ways.
When the player whose turn it is to play has just one card, and that card is the correct rank to match the lead (or if it is that player's turn to lead to a new stack), the player wins the game.
Sandipan Tarafdar describes a variant called Bluff played in West Bengal. The rules are the same as above, except that a player may play more than one card in a turn, declaring all the played cards to be of the currently required rank. When starting a new round a player choose any rank and play any number of cards declaring them all to be of that rank - for example three sevens. A player who wishes to challenge does so by saying "Bluff".
Shruti Raghavan reports that Bluff is sometimes played with a pack including jokers. In this case the jokers are wild and are always the truth, no matter what rank is supposed to be played.
In Bluff, a player who has passed is not allowed to put down cards again in that round, though they are still allowed to challenge.
Rather than ending as soon as the first player has run out of cards, the play may be continued until only one player has cards left. In this case the first player who ran out of cards wins, the next takes second place, and so on, with the last player holding cards as the loser.
Tactics. It is an advantage to start rounds, as the player who does so can choose what rank to play. If a player has many cards of a certian rank, he or she should choose that rank for that round. An often used strategy is to lie about your cards the first time you play them and tell the truth the second or third time. This way, your opponents have no idea whether or not you're telling the truth.
Hwei Yin invented the "force" option to make two-player games possible. This variation makes the pace slower and more intense, and, although still hilarious, "force" strategies may get too subtle for young children.
When playing this variation there are two ways of challenging. The challenger must say either "doubt" or "force". If the challenger says "doubt" the challenge is resolved as explained above. If the challenger says "force", the person whose play was challenged must produce from his hand a card whose rank matches the announced rank of the lead. If such a card is produced, then the challenger must pick up both that card and the stack, and the challenged player leads the next round. If the challenged player fails to produce such a card, he must pick up the stack and the challenger leads.
A player who has just played his last card may be "doubted" but cannot be "forced".
The key to winning (with or without the "force" variation) is getting the lead and setting the rank to your preference. This is done by winning challenges or ensuring that your card is the last played on the stack.
Eventually one person tends to collect all cards of a given rank. This is especially dangerous in the basic game: if this person gets the lead, she knows that everyone else must pass, so it's easier for her to sneak junk in as she dumps several cards uninterrupted.
The essential quandary for "forcing" comes when you have only one card that matches the lead. If you play it, then someone can "force" you and you'll lose the challenge. If you lie and play something else then you are safe from a force, but you might be doubted instead. After being stung with a few forces, people often don't have the guts to play at all with only one matching card.
Like all bluffing games, IDI essentially becomes a game of pattern recognition. The player who wins exploits patterns in her opponent's play before they can adjust. Thus, a bad player can hand the game to the same person every time by repeatedly challenging her and losing. This also means that two player games are very intense, as each player has only one other personality to concentrate on.
Here is David Zechiel's "Tierney family version" of I Doubt It, known as Liars Poker, though it is an entirely different game from the Liars Poker (Poker Menteur) on gambiter.com.
Another description of this game, rejoicing in the name "Fourshit", can be found on Khopesh's Bullshit page.
Calvin Yoshitake has developed a variation Cal's BS in which the play is in any order rather than in turn and two jokers are added to the deck.
On this site, there are pages on the very similar Russian game Verish' ne verish' and the related game Bullshit, in which the rank of cards played changes by one on each turn.