The harder places to hit are smaller and more points. Also, for the bulls eye, it needs to be a circle because it's an eye! by layout if you mean the way the numbers are arranged...
- It's done mainly to punish inaccuracy i.e if your aiming for 20 there is a chance of hitting 1 or 5 on either side.
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-No there is no mathematical reasoning for the numbers on a dart boar, Its funny you asked that question really, becaus ei spend all my time spending countless hours playing darts and studying the ddart board, but i have never come across a mathematical reasoning for it. :)
the 20 is placed at the top, next to 1 and the 5, because most people tend to go for the triple 20 as it is the highest score, and if they miss the penalty is that they get the lower score of 5 or 1, if the 19 or even the 15 were right next to the 20 it wouldn't be very exiting as even if the player was not very accurate, if they coud just aim it in the right general direction. But with the current layout, you have to be acurate to be good