A method is set forth for playing a bonus game in a secondary slot machine adjacent a primary slot machine. The primary slot machine issues a bonus qualifying signal to the secondary slot machine to start play of a bonus game when a bonus qualifying event occurs. The reels of the bonus game include value symbols, null symbols, and end game symbols which may be of two basic types: a lose game symbol and a stop game symbol. After the random spin, the values of any value symbols displayed on the payline of the secondary slot machine are accumulated into an accumulated winning value. The value symbols could include positive integer values, negative integer values, and multiples. The random spinning, determination of values of any-value symbol and the accumulation of a winning value is repeatedly continued until an end of the bonus game occurs.