  We present quantitative relations between work and information that are valid
both for finite sized and internally correlated systems as well in the
thermodynamical limit. We suggest work extraction should be viewed as a game
where the amount of work an agent can extract depends on how well it can guess
the micro-state of the system. In general it depends both on the agent's
knowledge and risk-tolerance, because the agent can bet on facts that are not
certain and thereby risk failure of the work extraction. We derive strikingly
simple expressions for the extractable work in the extreme cases of effectively
zero- and arbitrary risk tolerance respectively, thereby enveloping all cases.
Our derivation makes a connection between heat engines and the smooth entropy
approach. The latter has recently extended Shannon theory to encompass finite
sized and internally correlated bit strings, and our analysis points the way to
an analogous extension of statistical mechanics.
