Optimize speed and footprint of method

I'm writing a program for an embedded device based on the game of Darts, I'm writing code for a "Computer" player, basically I generate a series of random scores so that the computer tries to go from 501 down to zero, all is pretty straight forward till the score goes below 170, this is the number which in Darts you can checkout and finish on a double for example "40 = double 20, 16 = double 8 and so on...", I have an array "Checkoutcodes" which I can query for combinations of numbers which will allow the computer to finish the game, for example 145 = "t20t15d20" which translates to (3x20, 3x15, 2x20) which is 145 and game over. Now obviously in the real world it's not possible to get out every time so I have wrote code to mimic an attempt to checkout. These numbers represent the order on a dart board in a circular pattern, note the 5 is beside the 20 20,1,18,4,13,6,10,15,2,17,3,19,7,16,8,11,14,9,12,5 In order to mimic an attempt I randomly select the number needed or a number to the left or right, so for 145, and for the first part "t20", The computer could potentially hit a 1,20,5 or (3x1),(3x20),(3x5). Now if it selects a number other than "t20" then I'd have to retrieve a new checkout code, so if a (3x5) was hit, the score remaining would be 130 and the new checkout code would be "t20t20d5". This would repeat until 3 darts were thrown and at the end my code would evaluate the total score remaining against what it expected to be remaining. If they don't equal then I loop back and try again, this works ok when tested on a PC but when loaded onto an embedded device it's sluggishly slow. Below further explains the flow of how my code works. //Successful mimic 145 - "t20t15d20" - (3x20) hit 85 - "t19d14" - (1x7) hit 78 - "t18d12" - (3x4) hit Outcome is 66, expected was 66 so (3x20),(1x7),(3x4) is a valid combination //Unsuccessful mimic 145 - "t20t15d20" - (1x5) hit 140 - "t20t20d10" - (3x20) hit 80 - "t20d10" - (1x1) hit Outcome is 79, expected was 66 so (1x5),(3x20),(1x1) is not a valid combination, so code will loop till a valid combination is found. I need a way of retrieving these mimic combinations quickly on an embedded device, the full list of checkout code is attached.