Before we get to my new degenerate Strike strategy, here’s a brief history of the other times I’ve tried to take the analytics approach to the childhood activities of little league baseball and gym class.
To be clear, I was certainly never in little league. I think that’s a class of play that requires try outs and skill. This was more a municipal recreational league that accepted all who asked. I don’t know what age it was, but it was just at the point where the league was letting the kids pitch on their own.
But they weren’t very good. And, well, that was my whole strategy. If I swing, there’s a chance of a strike. If I don’t swing, there’s a fairly strong chance of a ball. My young mind’s conclusion? Don’t swing. Ever. My on base percentage was great! Then, inevitably, the next batter would strike out, ground out, fly out, or get out in some other way that let down the person on first base who had tried so not very hard to get there. (A teammate eventually tried to get me to swing, betting me some baseball card I very much wanted at the time. I struck out that at bat. There was at least one foul ball to redeem for the card, but I’m still waiting on him to pay up, as he claimed he was looking the other way and missed it.)
The next time was an obstacle course. In a high school gym glass, the teacher had set up 6 or 7 or 8 stations around the gym and one at a time, he would clock us as we attempted to do 10 sets of this or 15 reps of that around the gym, one after another, and your time would equate to a grade. But here’s the thing. My class was fairly late in the day. At that point word had spread about how good a certain other classmate had done, someone who a few years later would have multi-sport Division I scholarship offers and a few years after that a Super Bowl ring. So I listened carefully as the teacher explained the time penalty for each missed rep. If one of your reps was deemed incomplete, that’s a 2 second penalty instead. Or this other one is 5 seconds. Maybe “penalty” isn’t the right word, as it was a conversion. If I did 9 reps instead of 10, I’m billed 2 seconds for the rep I did not complete.
So I did the math. If I didn’t participate or attempt any of the stations, I would have a faster time than the aforementioned classmate whose time was the envy of the students around me. This teacher assigned letter grades based on how well you did, but also graded on a curve. If I recall correctly, I got an A for running a lap around the gym and not trying.
For Strike, the “best” strategy, will vary depending upon the number of dice in the arena. (It will also vary upon your goal and what you think is “best”, but let’s assume our sole goal is winning, despite that often being secondary or tertiary.) In discussing with some friends, I’ve concluded that the best strategy if there is a single die in the arena is to hurl your dice as hard as you can at the other die the arena, hoping they both exit the box.
Let me explain how I got here.
Billy Beane’s Moneyball strategy wasn’t far off what I’d stumbled upon in my short-lived, .000 batting average, baseball career: the game is a war of attrition, and what you are attriting is the opposing pitchers’ arms. If we were to make a Strike analogy, I’d argue that it is a fool’s errand to focus on going for matches. It’s a war of attrition and what you’re attriting is the other player’s die pool. The more frequently we can empty the arena, such that the opponent is forced to throw all of their dice in, the better! This ensures the quickest depletion of their dice pool.
Thusly, our goal is to empty the arena. (Corollarily, we’re also never going to spend more than 1 die a turn.)
Let’s start from a basic experiment. With 1 die in the arena, and 1 in hand to throw in, what is our strategy? Traditionally, I’d argue an average player’s strategy has been not to hit the die in the arena, as you risk it turning to an “X”, making it harder to create a pair with your die result. But! Friendly reminder that our goal is not necessarily to create pairs which would put dice back into our hands; rather, it is to empty the arena! As such, an “X” pair is as good as a “3” pair.
Further, perhaps we should re-state our goal as trying to leave as few dice in the arena as possible, as this will decrease the odds of the next player creating matches. When we do that, it becomes clearer that if we don’t get a match, it is still better for one of the dice to be an “X”, and hence, we def. are going to be hitting the die in the arena.
Hold on, let’s do the math.
There’s one die in the arena. Let’s say it shows “#” (any non “X” face). The odds that our dice will match, if we don’t hit the existing die, are 1/6. Because we don’t care about what the match is, we can hit the die in there to increase the chances of at least one “X”, and, our chances of a match are still 1/6!
But wait. What if you throw your die in so hard that it changes the face of the die in the arena, and your die bounces out. (On purpose!) Now we have a 1/6 chance of leaving the arena empty, but more importantly, we’ve shrunken the odds of leaving 2 dice in the arena to 0.
Maybe we should look at it not only through the odds of a match, but how many dice are left in the arena. Given 1 die in the pot, should you hit it, avoid it, or hit it such that you bounce your die out?
Playing by what you’d imagine is the spirit of the rules looks like a sucker’s game, with little chance of a match and a greater than 50% chance of leaving two dice! But, with our intentional bounce-out, things are starting to look a bit better. We’re almost there. We’ve gotten rid of the chances of 2 dice, but can we eliminate the possibility of even 1 die? Is there a 4th row to consider in that table? Sure. THROW IT EVEN HARDER.
Listen carefully, as this bit is the crutch of the strategy. After this it’s the boring probability bits; this is where I propose something preposterous, that couldn’t possibly work. And, I’m not saying it makes for a robust game, but!: if you can peg the single die hard enough that both it and your die fly out of the arena, you ensure the next player has to do the full dump, and you’ve only spent a single die! That’s some great ROI!
But it doesn’t sound…interesting. Also, did I buy this strategy at the Jerk Store? I’m not interested in taking the fun out of the game or introducing targeted attacks on the next player, but if there’s an objectively superior strategy, I can’t just ignore it.
Can we measure the probabilities on it? Well, no. With almost certainty though we’ve collapsed the probably of leaving two dice or taking two dice onto the odds that we leave one in the arena. The unknown is our aim, the angle, what force…how do we get the static die to leap out of its socks and land over there under the couch. From my experiments so far…it is possible. (So far, my shortcoming has been aim –why, oh why, did I not practice swinging as a child!– but we’ll get more into that further below.)
How do you feel? Are you ok with the forceful gameplay gameplan that cruts across this parking lot? (What do you call it when you drive willy-nilly through the empty bits of a parking lot, without regards to lane lines, running counter to the designer’s intents. My family calls it ‘crutting’.)
I think we’ve made remarkable progress regarding what to do with 1 die in the arena, but that won’t be the only situation we face. We’ll need to consider what we want to do when there are 2, 3, 4, or 5 dice in the arena. We’re in agreement that the current plan is “Get it down to fewer dice for the next player”, right?
Let’s run some more numbers. What happens if we’re faced with two dice in the arena?
Now we have some things to think about. Look at those odds of increasing your hand size compared to only 1 die in the arena. But I’m not thinking about it from the stand point of what my strategy is when there are 2 in the arena: no, this is strengthening my resolve to not leave 2 in the bowl for you! Rewind. If I hit or don’t hit a single die in the arena, there is a >50% chance of two dice in the bowl for the next play, which translates to a >40% chance of increasing your hand size, and that’s too high for my blood.
I’m of the mind that Strike is an offensive game to be played in a way that you aim to leave as few dice as possible in the arena for the next player, without regards to building your own hand size. With 1 die in the pool, the next player’s best chance of increasing their hand size is 16%, but with 2, it can go above 40%! FORTY!
But let’s look at that 2-Dice chart again, and look at what happens if we consider the bounce: we’ve increased the odds of leaving 2 dice for our opponent to 67%! The whole reason we’re innovating this hurling tactic is to lower that number to 0, so the “bounce” throw is out for 2 dice in the arena, and I won’t dwell on it, but it’s actually out for any scenario other than 1 die in the arena.
Strategy this far: If 1 die is in the pit, hit it hard enough to bounce both out. If 2, try to hit both, but make sure you hit at least one.
“What about 3 dice in the arena?” As my favorite college stats professor used to say, and probably still does, when a student asks him a question, “*GASP* I don’t know, let’s find out!” (He knew; he always knew.)
By now I think we have see enough of a pattern, and have taxed enough of my probability muscles, that we know what to do: hit as many as you can. There’s a bit of a reason to keep one un-hit if you’re in a position where your hand size is critically low, but otherwise, knock them all around! “Strike” them, you could say. They don’t have to go home with you, but they can’t stay in the arena.
Maybe, it turns out, there’s a reason why the game is called Strike. I mean, you know what “strike” means outside of its Ravensburger context: hit something!
It is right there in the name.
It’s also right there on the box. Here’s the cover photo for the edition I have.
They’re all bouncing out! Wait…is this the intended strategy? Was the treasure map printed on the back of the directions to the big W the whole time? It’s been right there under our noses! That die coming out of the box at us has hit the other dice with enough force that it looks like we might get a couple other escapees as well. (Don’t mind that the box cover as an actual game state would imply that there had been 6 dice in the arena at the start of your turn, an impossible situation.)
Unfortunately, my ability to execute this strategy, is a bowling GIF that is less Pete Weber and more…
Here are some practice shots.
That said, I’ve tried this now in 7 or so games, and I’m convinced. I may not have won all 7, but I was flirtatiously competitive, and, at the time, I hadn’t quite worked out what I wanted to do for 2+ in the arena. I’m in for the long haul, as I refine my skills to something like…
In the meantime, my fellow players seem to get sufficient entertainment out of my bizarre approach, that, combined with my woeful aim, fun was had by all.
Which…is what makes me happy. As I said, winning is not necessarily my top priority, but, like attempting an edge-case strategy in many games, there’s an allure of the “what if…..” whimsy of such an unintuitive strategy. I’m sold that this strategy is brilliant, and there’s even more joy to be had when the other players aren’t buying it!
The difficulty, from my standpoint, of course, is execution…and that’s also what makes me happy. What I didn’t want, was to take the soul out of the game and turn it into a rote exercise where we each robotically (hey, like that orange one above!) hurl the dice as hard as we can at the single die, and suck the life out of the game –the lure of “just one more die…”, as you mentally fall for so many logical fallacies, entranced by the gamble.
Could you just look at the probabilities and take the fun out of Strike? Of course not – the game is impossibly fun, in the sense that you can’t possibly do it!
Which brings us to…well, this:
In my struggling efforts to hit the lone die, we did come across this die… Seven games into the “knock the dice together as hard as you can strategy”, and a pip had gone missing. Coincidence? Now, I feel compelled to point out that there were no eye witnesses to the pip’s disappearance. And besides, my aim was demonstrably off such that there weren’t many collusions which could have caused its dislodgement, your honor.
Perhaps I doth protest too much.
Anyway, I scheduled this post for the day before Thanksgiving in the U.S. on purpose. Maybe pull this off the shelf to enjoy with the folks that live in your house over the holiday and enjoy the whimsy of a new approach.
Oh, and be safe.
Note: For a full review, see Dale’s recent post here.
To quote Toy Story: “Not a Flying Toy.”
Excellent article, James… I still have flashbacks to playing Strike with you last month.
I love that robotic “bowler”!
I’m a firm believer that if you create rules for a competition and you leave a loophole that someone exploits, that’s your fault and not the fault of the person smart enough to exploit it. If I had been your gym teacher, I would have congratulated you on your insight (and math skills), given you an A, and then immediately changed the rules.
This extends to real-life situations, both important ones (including, sadly, elections) and less vital ones (like sports). You see sports teams tanking (i.e., deliberately trying to lose) to gain a competitive advantage. They are frequently castigated for this, but if the rules encourage it and it works, them stop wringing your hands and change the damn rules! Any gamer will tell you that it’s the scoring rules that determines how you play, so change them to encourage the behavior you want to see.