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A game with several players in which the outcome is determined not only by the skill of the players but also by random factors (shuffling cards, throwing a dice, etc.). Investigations of drawing room games (mainly card games) occupy an important position in the theory of games (cf. [[Games, theory of|Games, theory of]]). Drawing room games are, on the one hand, an inexhaustible source of mathematically interesting models of games and, on the other, they are models of more serious conflicts — war, economics, etc. Poker, the first model of which was investigated by J. von Neumann in 1928 (see [[#References|[1]]]), played a role at the beginning of the theory of games that is analogous to the role of dice games in probability theory. Later many special models of poker-type games were constructed and solved, and in the 1950s S. Karlin and R. Restrepo laid the foundations of the general theory of  "poker" -type two-person zero-sum games (cf. [[Two-person zero-sum game|Two-person zero-sum game]]). In models of them a player I (respectively, II) knows his card <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340201.png" /> (respectively, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340202.png" />), which is the realization of a random variable having a distribution <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340203.png" /> (respectively, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340204.png" />). The strategies (cf. [[Strategy (in game theory)|Strategy (in game theory)]]) of the players I and II are vectors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340205.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340206.png" />, and the pay-off function has the form

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340207.png" /></td> </tr></table>

Karlin and Restrepo found sufficient effective methods for solving games like this (see [[#References|[2]]]).

Many investigations have been devoted to bridge. Since in bridge two partners are, in fact, a single player, it is an example of a game without complete memory.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J. von Neumann,   "Zur Theorie der Gesellschaftsspiele"  ''Math. Ann'' , '''100'''  (1928)  pp. 295–320</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  S. Karlin,   "Mathematical methods and theory in games, programming and economics" , Addison-Wesley  (1959)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  G.L. Thompson,   "Signaling strategies in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340208.png" />-person games" , ''Contributions to the theory of games'' , '''2''' , Princeton Univ. Press  (1953)  pp. 267–277</TD></TR></table>