There are certain points in the game where you do know whether you will win or not, if you're on 5 and want to win, take 2 counters, if it’s your turn and you're on 3 you can’t do anything and will lose. For example if you are on 5 and want to win you can put your opponent in a checkmate position by taking 2 counters forcing it to be their turn with 3 counters and as noted before 3 is a checkmate number therefore leaving you with a win. I know this as there is. I found out that whenever it is your turn and you are on 7 or 5 if you make the right move then you will automatically win. To win on 7 take 1 to win and on 5 take 2 and to win. When your on 7 and it’s your turn and you take 1 counter and your opponent takes 2 counters (leaving the number at 4) the best way to win is to take one and therefore forcing 3 which is a point of the game where you automatically win.
The best way to win is to be player 1 and from the start is by taking 1 counter, from there your opponent has the option to either take 1 or 2 counters. If they take two counters then you must take one counter, therefore leaving them with the ‘checkmate’ number which is 3, from there they have to pick 1 or 2 which cannot win the game and based on what they pick make sure on your next turn you choose the number that will enable you to win the game. If the opponent is player 2 and chooses 2 as their first turn then your left with 4 counters left, the best option would be to take 1 counter as this leaves the opponent with 3 or as said before the ‘checkmate’ number and so once it is their turn they are left to pick 1 or 2 which cannot win the game therefore meaning your next turn would be best played if you take 1 or 2 counters to win the game based on what they do.
I think it does matter who has their turn first as there is a certain strategy which can be used to win right from the start but the strategy will only work if the person going first takes 1 counter and then they continue the strategy based on what the opponent does. If both players don’t have knowledge of the strategy then it may or may not matter who goes first as both players would not be aware of the strategy therefore meaning the person going first may choose to take 2 counters and so on meaning whatever they choose could lead to different results and the winner wouldn’t always the first person to take their turn. It also depends on the knowledge of each player and whether they would be able to make the right move in certain situations and be able to understand and adapt quick enough due to the opponents moves.
Here is a image showing the strategy which guarantees a win from the start -