Blitz Bowl: Game State Puzzle (Humans and Goblins)

"The Crush" podcast has a "game-state-puzzles" channel on their Discord channel.  I recently added a game state puzzle featuring Humans and Goblins:

All players on the board are shown. You are the Humans and it's the start of your turn, challenge cards are as shown. Maximize the expected value of points this turn. Let's go with regular 3 point touchdowns. 

Extra Credit #1: If you could replace one of the cards with "Break Some Bones!", 1) would you, and if yes, 2a) which one would you replace, and 2b) how does that impact your solution (expected value of points this turn)?

A number of great responses were provided, but the best and most comprehensive was given by LanguiDude (Dan), who took a very scholarly approach writing out a complete examination of the puzzle.  Here is his fun and well-thought-out analysis:

Game State Challenge #1: Extra Credit
Or: On Swapping In Break Some Bones, A Treatise

It is assumed that if you are reading this essay, you are familiar with Mezmaron's Game State Challenge #1, on the Discord channel for the Blitz Bowl podcast: The Crush! The question posed was "would you swap in Break Some Bones (BSB) for one of the cards given? If so, which card, and how does that impact your expected points?" For a definitive answer, I will first address the scenario without a swap, then I will assess each card, one after the other. I will make one dangerous assumption for this essay: everything goes according to plan. (Ignore that sound, it is merely Nuffle’s laughter…)

Let’s begin by discussing the basic scenario, without swapping in Break Some Bones! As [@SC Matt] and I both agree, the best way this turn could play out is by Marking with the open Lineman to score Tie Them Up! (+2 points, and Inspiration.) Then Sidestep with the Catcher to gain Go Deep! (+2 points.) Finally, attempt a Throw with the Thrower to be received by the Catcher. Using a combination of luck and Raw Talent (and potentially Inspiration, if things go kind of wrong) this should result in scoring Show Us a Completion (+1 point and an additional +2 for a Clean Sweep), and a touchdown (+3 points.) Given this sequence of events, I will have scored a whopping 10 points! As long as my score was equal to or greater than my opponents, this will give me a Sudden Death victory. But even if I'm behind, I'll have closed the gap significantly...

Before discussing the cards I'd actually swap, let's discuss how I would score BSB. This doesn't change from one scenario to the next, so it will provide a convenient shorthand for when I say "score BSB." In every case, I will block with the Lineman Assisted by the Catcher. This will give me two blocking dice to roll, and as every roll results in a Knock Down (with the exception of the dreaded Double Skull!) I have a 35/36 chance of knocking down the Goblin. Finally, because Goblins have armor 6+, the odds of not scoring BSB is 1/216, or ~.4%. [Permit me, dear reader, to point out that I got a solid C in statistics.]

In addressing the cards individually I will discuss them in the order I would least like to swap them. First: Go Deep! Because Go Deep! has Raw Talent on the back (and I really like Raw Talent to increase my odds at a successful completion/touchdown combo), this is the card I'd be least likely to swap. Nevertheless, this is what the turn would look like given this swap. [Remember our assumption: everything goes according to plan.] First move, I'd mark with the open Lineman to score Tie Them Up (+2 points, and Inspiration). Then I'd score BSB (as outlined in the above paragraph) for +3 points. Finally, I'd attempt the pass/touchdown combo, scoring Show Us A Completion (+1 point, and +2 for Clean Sweep), and a touchdown using Catcher’s Instincts (+3 points) for a total of 11 points.

Next, Tie Them Up! Originally, I had thought I would least like to swap this card. Even if I didn't use the bonus play - Inspiration - this turn to score a touchdown, it would certainly come in handy in the future. After considering how important Go Deep! is to the round, however, it is clear that this card is not as important as Go Deep! in regards to the turn in discussion. With Tie Them Up gone, I no longer need to spend my first action marking with my lineman. So my first action will be to score BSB (+3 points). Then I would Run the Catcher next to the endzone, which would get me Go Deep! (+2 points and Raw Talent). Finally, I would attempt the pass, to score Show Us A Completion (+1 points, and Clean Sweep +2 points), then get the touchdown with Catcher's Instincts (+3 points). Total points scored: 11. This is a fine place to be in, and as I have a shot at Blocking Play, it's not the worst card to trade.

Finally, let's discuss Show Us A Completion! This would be my preferred card to Trade for BSB. Namely because it yields the greatest increase in points. (2 points net, to be precise.) While it’s a little tricky to pull off the Clean Sweep in this configuration, I will attempt to show that it’s no trickier than the basic scenario. The first move is still Tie Them Up. The two remaining cards are Go Deep, and BSB. If I Go Deep with my catcher right now, I'm left attempting BSB without assistance. This isn't the worst move ever, but it's definitely risky. So the second move is to score BSB. To wrap it up, I score the final card, Go Deep, and get the clean sweep. All that’s left is the touchdown. Given our initial assumption, “everything going to plan” in this case means I have Inspiration from Tie Them Up, and Raw Talent from Go Deep., and can still score a touchdown with my fourth action, passing the ball to the Catcher, and using Catcher's Instinct to finish the play. Whichever way I play it out, if all goes according to plan, I will have scored an admirable 12 points.

All of these swaps have potential for an increase in points. However, the first two, as I mentioned above, are significantly worse than Show Us A Completion. Tie Them Up and Go Deep both are "automatic" point-earners, in that they don't rely on you rolling anything. So I would not choose to swap either of those for BSB. Which leaves SUAC. As SUAC is arguably a more difficult card to guarantee than BSB, I would definitely trade this card, if I had to trade a card. That being said, the fact that I can only get a Clean Sweep and a touchdown by getting Inspiration (and it’s only a 50% chance, at that) I would much rather keep the initial scenario as presented.

I hope to propose additional game-state puzzles soon.  I believe they really demonstrate that Blitz Bowl, although simple to learn, offers much more strategy, analysis, and complexity than first meets the eye. This "easy to learn and difficult to master" aspect is one thing I love about the game of Blitz Bowl.