State lawmakers are betting on the whirl of a spinning roulette wheel, the rattle of poker chips, and lady luck to bring in new tax dollars as they look to expand gaming capabilities amid deepening financial deficits.

The strategy is paying off. In 2011, the states that saw the largest increases in tax revenue were those where new casinos opened during that year or had a full year of operations. This included Kansas, which saw a 38% bump, and ...