Gaming machines with bonusing

1. A method of operating a gaming machine, said method comprising:

(a) randomly generating a combination of game symbols from a plurality of game symbols, said plurality of game symbols at least including a plurality of different award value game symbols and a plurality of end game symbols, said end game symbols being predetermined prior to any random generation of the combination of game symbols,

(b) causing a display of the gaming machine to display:

(i) the randomly generated combination of game symbols, and

(ii) for each of any randomly generated award value game symbols of the randomly generated combination of game symbols, an individual numerical award value associated with said randomly generated award value game symbol,

(c) summing the individual displayed numerical award values associated with any displayed award value game symbols to form an accumulated winnings value,

(d) repeating steps (a) and (c) until a predetermined number of said end game symbols have been randomly generated in the generated combinations of game symbols, said predetermined number being at least one, and

(e) ending play when the predetermined number is reached.

2. The method of claim 1 , wherein the plurality of game symbols includes a plurality of null game symbols.

3. The method of claim 1 wherein the award value game symbols include positive integer values.

4. The method of claim 1 wherein the award value game symbols include negative integer values.

5. The method of claim 1 further comprising:

ending play when a player stop signal is received in response to the step of summing, and awarding the accumulated winnings value in response to the received player stop signal.

6. The method of claim 1 further comprising:

determining when the accumulated winnings value at least equals a predetermined winnings value, ending play when the accumulated winnings value at least equals the predetermined winnings value, and awarding the accumulated winnings value.

7. A method of operating a gaming machine, said method comprising:

(a) randomly generating a combination of game symbols from a plurality of game symbols for a play of a bonus game, said plurality of game symbols at least including a plurality of different award value game symbols and at least one end game symbol, said at least one end game symbol being predetermined prior to any random generation of the combination of game symbols,

(b) causing a display device to display:

(i) the randomly generated combination of game symbols, and

(ii) for each of any randomly generated award value game symbols of the randomly generated combination of game symbols, an individual numerical award value associated with said randomly generated award value game symbol,

(c) for the play of the bonus game, summing the individual displayed numerical award values associated with any randomly generated award value game symbols to form an accumulated winnings value, and

(d) repeating (a) to (c) until ending the play of the bonus game when either one of: (i) the formed accumulated winnings value reaches a predetermined value greater than zero, or (ii) at least one of said end game symbols is randomly generated in at least one of the randomly generated combinations of game symbols.

8. The method of claim 7 further comprising:

paying an award different from the predetermined value in response to ending the play of the bonus game.

9. The method of claim 7 further comprising:

paying a progressive jackpot in response to ending the play of the bonus game.

10. The method of claim 7 further comprising:

paying the predetermined value in response to ending the play of the bonus game.

11. A method of operating a gaming machine, said method comprising:

(a) setting a count value to zero when a casino bonus game starts,

(b) randomly generating a combination of game symbols from a plurality of game symbols, said plurality of game symbols including at least one end game symbol which is predetermined prior to any random generation of the combination of game symbols,

(c) causing a display device of the gaming machine to display the randomly generated combination of game symbols,

(d) incrementing the count value, and

(e) repeating (b) to (d) until ending the play of the casino bonus game when either one of: (i) the at least one end game symbol is randomly generated in one of the generated combinations of game symbols, or (ii) a predetermined value for the count value is reached, said predetermined value for the count value being at least one.

12. The method of claim 11 further comprising;

paying a jackpot bonus in response to ending the casino bonus game.

13. A method of operating a casino gaming machine, said method comprising:

upon an occurrence of a bonus qualifying signal during a play of a primary casino game:

(a) summing any individual displayed numerical award values associated with any randomly generated award value symbols displayed by a display of the casino gaming machine to an accumulated award value during a play of a casino bonus game,

(b) receiving a player stop signal from a player input of the casino gaming machine during the play of the casino bonus game,

(c) causing the display of the casino gaming machine to display an end bonus game symbol during the play of the casino bonus game, said end game symbol being predetermined prior to any random generation of the award value symbols,

(d) awarding at least the accumulated award value in response to receiving the player stop signal and before the end bonus game symbol is displayed, and

(e) ending the play of the casino bonus game in response to either one of: (i) awarding the accumulated award value, or (ii) displaying the end bonus game symbol before receiving the player stop signal.

14. The method of claim 13 wherein the value symbols include negative integer values.

15. The method of claim 13 wherein the value symbols include multipliers.