A gaming server device may conduct a networked bingo game with client devices, each client device associated with a respective bingo ticket. Conducting the game may involve: (i) randomly selecting symbols from the symbol set, (ii) marking the selected symbols on any bingo tickets that contain the selected symbols, and (iii) repeating the random selecting and marking until one or more of the bingo tickets are marked with a winning pattern. The gaming server device may transmit an offer to a particular client device associated with a particular bingo ticket that is not marked with the winning pattern. The offer may be for the gaming server device to randomly select a further symbol from the symbol set at a cost to the particular client device, where the cost is based on an expected gain that acceptance of the offer provides to the particular client device.