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To win 'got it', there are certain numbers you have to get to first.
Your target is 18. If you get this, you've already won. Any move the computer makes after 18 will not be enough for 23, instead helping you to get 23.
First, start off with three.
The highest the computer can then get to is 7. You have to get to 8.
The computer will go again, and the highest it can get to is 12. Using this, get to 13.
Any move the computer makes from here will help get you to 18, the target number. The highest it can move is 17.
From here get to 18. After this, there is a number of combinations to get you to 23 for victory:
1(computer)+4(you) or 19+4
2+3 or 20+3
3+2 or 21+2
4+1 or 22+1
As you can see, no matter what the computer does, it cannot prevent you from winning if you get to 18 first. Consequently, you will win!