You have the chance to play the following game. Each round cost £4 and you win £???? per round, where ???? is your score for that round. You can play as many rounds as you like. ]

Each round is as follows - 

You roll a dice. If the dice lands on 3 then you can roll again, if it lands on anything else then you stop. Your score for the round is the total of all your rolls in that round. 

e.g.

  First round  

Roll 5, STOP 

Round Score 5 

Second round  

Roll 3, Roll 3, Roll 1, STOP 

Round Score 3+3+1 = 7 

Third round 

Roll 1, STOP 

Round Score 1 

Total score after 3 rounds of 5+7+1 = 13 

Therefore, you made a profit of £1 in total, as you played 3 rounds costing £12, but won back £13. 

a) Given that you have plenty of money to play with, would you keep playing the game? Use a simulation to decide. 

b) If the game is changed so that you can continue to roll on a 1 instead of a 3. Would this affect the choice of whether you would play?