The trouble with consumer goods such as board game is that there is a lot of emotional value involved. This means that it is very difficult for you to ascertain the value you are bringing to your customers.
Years ago, I read this book Setting Profitable Prices by Marlene Jensen. There is one strategy that caught my eye, but you will have to assess whether is it relevant to the situation that you have.
The strategy is to run tests on several versions of your website, and evaluate the best click-through or transactions.
For example, say you want to test a price point of $19.95, $24.95, and $29.95. Set up 3 landing pages with the exact same information and design. Only the prices in these 3 landing pages are different. Then spend a little money to advertise the landing pages in FB or Google. Track things like the click, heat maps and of course the conversion.
There is one thing you need to take note: Make sure the default landing page - i.e. the one that you can navigate to from your home page, is the one with the highest price. There are visitors who tend to check out the website before making the purchase. You do not want to direct someone to a page with $29.95, but your home page links to a page with $19.95 pricing.
That's being said, I think this strategy is only worth it if you are going to spend a lot of money in advertising. Because you need lots of data points.
If this is not relevant, here are some general rule of thumb in pricing:
1) If in doubt, always price your product higher. It is extremely easy for you to give discount. In the situation that you are not able to generate enough sales at a higher price point, you can lower the price, and then offer a partial refund to those who have purchased from you at a higher price.
2) Find one great story about your product, and communicate it. Your customers do not just buy your board game to be entertained. They are buying something else. The story of your product, and how it relates to them. Having a great story will make it easier for you to price higher.
3) Competitor's price is a great guideline, but do not blindly follow it. Only use them to establish what's your positioning (high entertainment value, different target audience, simple and brainless game, etc).
Hope this will help you!