This group of games is characteristic of Russia and Scandinavia, and has also spread to China, Eastern Europe and in some cases worldwide. The object is to get rid of cards, by beating cards played by opponents.
As in trick taking games there is a ranking of cards, so that some cards beat others. The difference is that in a trick-taking game, if you cannot or do not wish to beat the previous card played to a trick, you play some other card which does not beat it. In a beating games, if you do not beat the previous card played, you are not allowed to play a card at all - you have to pick up the previous card (and sometimes other cards) and add it to your hand. During the game players will have different numbers of cards, and the object is generally to get rid of all your cards. Most of these games are played to find a loser rather than a winner, the loser being the last person left holding cards. Often the name of the game is the name given to the loser - for example in Russian games of this group the loser is the "fool" (дурак).
Beating games proper can be divided into four main groups. To this I add a fifth group of games which do not really involve beating, but employ a similar mechanism in that if you cannot play a card you must pick up.
A basic move consists of a card played by the attacker which is either beaten or picked up (possibly with other cards) by the defender.
The attack begins as in group 1, but if the attack card is beaten, the card used to beat it becomes an attack on the next player, who must in turn beat it or pick up, and so on round the table.
The attack consists of several cards played simultaneously. The next player may beat some or all of these cards; any that are unbeaten must be picked up.
The attack begins with a single card (or in some cases a group of equal cards). It can be continued by any opponent of the defender "throwing in" further cards equal in rank to any cards already played during the attack. If the defender does not beat all the attacking cards, including those thrown in, all the cards in the attack must be picked up by the defender, including the beaten attack acrds and the cards used to beat them.
These games have in common with the other games of this group that if you cannot play you have to pick up the pile of cards so far played, and the object is to get rid of cards. However, the rule as to which card(s) can be played is not a normal beating rule. You may have to play the next higher card in rank, or an equal card. These games also have the feature that the cards are played face down, and players may try to play cards that do not follow the rule but must pick up the pile if successfully challenged.
Alexander Konyukhov's page Правила игры в дурака has rules for over 40 Russian Fool games. His web site Durbetsel also has free software for playing these and other card games.