I recently bought the book Mathematics of Tabletop Games by Aaron Montgomery.

The book “…provides a bridge between mathematics and hobby tabletop gaming. Instead of focusing on games mathematicians play, such as nim and chomp, this book starts with the tabletop games played by avid gamers and hopes to address the question: which field of mathematics concerns itself with this situation?” Accessed 3/12/24 https://www.routledge.com/Mathematics-of-Tabletop-Games/Montgomery/p/book/9781032468525?srsltid=AfmBOoppHs-kRu-BHsRnkanT4JEnodORFs2Thgjq-J9q9bWxFkGCVpFC

I’m no mathematician, my maths skills are a bit rusty. But I’m getting very frustrated with the book within the first chapter.

After using the sum rule to determine how many cards are in the hard knocks deck in the game The Grizzled (I still need to get my copy to the table). The author Aaron Montgomery then poses the following question about the threat deck in the game:

“In the threat deck, there are 14 cards containing each of the three threats. How large is the deck of threat cards?”

So you stop and think what the answer could be based on the information given. Then instantly the author springs the following on you:

“While using the Sum Rule here might be tempting, that rule doesn’t apply since some threat cards contain more than one threat.”

This opening sentence of the author explaining the solution to me feels like the author is going “aha! You fell into my clever trap because you didn’t take into account …”

For me to have a proper attempt at answering the question you need to be presented with all the information. At no point in the question is it mentioned that cards could contain more than one threat. To me it implies that they don’t.

The example itself I like and explains the Counting with the Inclusion-Exclusion Principle very well. Well enough for me to grasp. But it’s that initial question not giving all the information needed that infuriates me.

My next bit of frustration is to do with applying the Permutation rule to the opening hand in a game of Scout.

“In the five-player game of SCOUT, each player is dealt nine cards from the deck of 45 unique cards and cannot change the order of the cards. A player will try to play a group of sequential cards in their hand stronger than the current combo (see page 82). The Permutation Rule can be used to determine that there are approximately 3 × 1014 opening hands:”

For me this only works and is correct if you deal the cards to each player nine cards in one go. But who the heck deals like this? I know it makes the maths more complicated for working out the number of combinations for the opening hand. But when normal people deal each player gets one card at a time. So the first player in a five player game would get cards 45, 40, 35,… not cards 45,44,43,…

Also doesn’t the example given only mean that this is the possible number of opening hands for the first player dealing in this abnormal way?

Is the way the cards are dealt irrelevant?

So what am I missing?

I’d ask the author but there are no social media or email details for the author. Maybe someone out there could explain to me in simple terms.