Why I Prefer Playing with the 2s, 3s, and 4s: A Mathematician’s Discussion

Why I Prefer Playing with the 2s, 3s, and 4s: A Mathematician’s Discussion

In Rook, it is very popular to remove the 2s, 3s, and 4s from each of the four colors.  This amounts to 12 cards less and 3 fewer rounds per game.   This makes each game shorter.  However, I have a suggestion as to why this takes away from inherent challenge of the game, and ultimately makes the luck factor much greater.

Each trump you have is 1 of 12 rather than 1 of 15.

A few years ago, I was playing basketball with a group of friends.  They said to me, I prefer playing 1s and 2s rather than playing 2s and 3s (meaning every basket is worth 1 point rather than 2 points and outside the arc is worth 2 points).    They said to me, “It’s just easier to keep track of scores.  It’s easier to count.”

I looked at them and replied, “But it makes 3-pointers more powerful. Instead of only being 50% more, they are worth 100% more.”  I then apologized saying I was a math major and that is just the way my mind works. 🙂

However, my line of thinking about 2s and 3s rings true when it comes to taking out the 2s, 3s, and 4s in Rook.

First of all when you remove 3 cards, you are taking about 12 out of 57 cards in the deck.   That is roughly 20% percent of the deck.  Secondly, it takes away 3 of the trumps.  that mean that every trump you have in your hand is 8% of the trumps in play.  If you start with 5 trumps in your hand at the very beginning, you already have 41% of the trumps in your hand.  If you were to lead one trump and a trump is played from each of the other 3 players, 8 trumps are already accounted for after round one.  That is 67% of the trumps.  Only 4 more trumps left.  So if you have the highest trump in your hand with 5 of a color, you are already at an extremely power position.

In addition, the kitty (or nest) is still up for the taking.  If you are allowed to exchange all 5 cards from the kitty into your hand, you have an opportunity to replace 45% of your hand (5 cards out of 11).  You have 5 more cards to potentially give you more trump.   There are 34 unknown cards in the deck (57 – 12 – 11).  So for example, if you started with 5 of one color, there are still 6 of that color and the rook left, 7 more trump.  That means that even though you have 5, you have a 20% chance that any random card is a trump.  Probably states that 1 out of the 5 cards in the kitty will be your trump color.

Thus, it is in your best interest to bid higher and higher to go for the kitty.  The kitty is so powerful.

But what makes this version of Rook more popular is the fact that there are those occasions where 4 or 5 of the cards in the kitty are no help whatsoever.

I enjoy bidding as there is certainly a lot of strategy at play during this stage of the game.  However, I feel the real fun of rook is in paying attention to who plays what and using this as a predictor as to what each player has.

When removing the 2s, 3s and 4s, you simply are taking away potential for strategy, card counting, and skill to be a big part of the game, and instead making the game much more about the luck of the draw.


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