Distributed/concurrent strategies have been introduced as special maps of event structures. As such they factor through their "rigid images", themselves strategies. By concentrating on such "rigid image" strategies we are able to give an elementary account of distributed strategies and their composition, resulting in a category of games and strategies. This is in contrast to the usual development where composition involves the pullback of event structures explicitly and results in a bicategory. It is shown how, in this simpler setting, to extend strategies to probabilistic strategies; and indicated how through probability we can track nondeterministic branching behaviour, that one might otherwise think lost irrevocably in restricting attention to "rigid image" strategies.