Abstract: In a gaming system, a central computer generates a plurality of game win-loss outcome stacks, each stack having at least one “win” (preferably, large-prize) outcome. Sub-stacks, from among the plurality of stacks, are transmitted to casino or other group controllers or computers, each casino controller being coupled to a plurality of gaming terminals. In response to placing a large-prize wager, in addition to normal, local game wager, a gaming terminal requests a large-prize outcome from the sub-stack which is stored in the casino controller. Whenever a casino controller's sub-stack is depleted, it requests a new sub-stack from the central computer. Preferably the central computer selects a new sub-stack for transmission according to a selection process which is weighted so as to maintain the ratio of winning outcomes to all outcomes in a predetermined range. When all sub-stacks of a given stack have been transmitted, the central computer generates a new stack to replace the depleted stack.