❖ Version History ❖

November – December, 2024
Okay friends…. buckle up…. we are going to talk about some beautiful math today.
(I can hear my girlfriend vomiting at the thought of this sentence).

So, previously on the Librarium Games Design Journal, we spent a good long while talking about a series of play tests that we have been doing, and the feedback that we have been getting from our friends as the play testing develops. In our last post we spent most of our time covering the visual changes that we would need to change in order to accommodate the requests, but we did not take much time to talk about the mechanical changes.

Today we are going to go over three topics on the mechanics of the game:
•The Pre-Dice Rolling Caveat
•The ‘Haggle’ Mechanic
•The ‘Betting’ Mechanic

The first two items on this list are fairly simple points in conversation… but the last one is something truly mesmerizing, and will forever change the experience of playing this game. So… without further adieu, let’s get into it!

Mechanical Adjustment #1 :: The Pre-Dice Rolling Caveat!
What is the Problem:
Sometimes a player will begin their turn with no silk tokens on the collaborative Tic-Tac-Toe board before they roll the dice. This effectively means that unless they roll doubles, they will make no income this turn AND they will set up the next player with a very high likelihood to earn a much larger profit than them. = Very Unsatisfying.

What is the Solution?
To help alleviate the stress of this scenario, we have created a ‘Caveat Rule’ (credit to Walter for this idea). We are calling it a ‘Caveat Rule’ because it is only ever going to be implemented when a player experiences this exact scenario. Here is how it will read: “If a player would start their turn with no silk on the silk tray, then they roll x1 10-sided dice for a complimentary silk to be placed on the board”. (the rule language will likely be condensed for the rule book, but you get the idea).

Mechanical Adjustment #2 :: The Haggle Mechanic!
What is the Problem:
Up until now, we have been letting every type of “Silk Pattern” card be openly available to purchase during your turn. This is an issue for a variety of subtle reasons… but in the end the most important idea to take away here is that ‘free access’ to anything you want to buy on your turn makes the game too easy & weighted in favor of those who have an advantage in the game. Ironically, the solution would be simple… just make it harder to buy things! But how to accomplish that actually took a lot of negotiating, especially for finding the most ‘fun’ way to solve the issue.

What is the Solution?
To fix this problem in a… ‘thematic way’, I actually specifically pictured myself shopping for fabrics at the flee market (I know this sounds crazy, but bear with me). More often than not, if you are looking through a merchant’s wares, especially big products (in my case I am picturing leather hides & Indian rugs), these items are spread out on a huge table for display… but there are only so many spaces on a table for these materials! If you wanted to see other options, you would need to wait your turn to speak with the merchant, and have them rotate the stock for you, moving some objects from the bottom of the pile onto the top!

We can simulate this exact scenario with our silk shop by taking all of the pattern cards, shuffling them into a deck, and then only revealing x3 cards at a time that are available for purchase. If you wanted to have other patterns available to you, you will have to throw a little coin at the merchant to convince them to bring out new patterns! (and hence, pull three new cards from the deck & place them on top of the other available cards that were already there). This not only solves our scarcity problem, it actually implements new strategies into the game as well! You see a pattern that you want, but cannot afford on your turn? Rotate the pile to hide it from the other players! – This promotes new techniques in the gameplay that give players agency & strategic use of their resources while also solving our problem of letting them have too much advantage previously! It’s a three-part victory!

And Finally, at Long Last:
Mechanical Adjustment #3 :: The Betting Mechanic!
What is the Problem:
A Player’s turn is… honestly sort of straightforward and boring: Roll Dice, Buy Things, End Turn. There is little to no strategy in the ‘rolling of the dice’ phase of this process. You are handed a scenario before your turn begins, you interact with that scenario using the dice to randomly generate numbers, and you hope that things are going to work out in your favor. If the board that was handed to you was not terribly good, then there are big issues with the excitement that you have for not only your turn, but also your entire goal in the game & sense of victory.

What is the Solution?
Thanks to a crazy conversation that I had with our friend Tom during one of our play tests, we got to chit-chatting about this idea and what other options a player might even have. Somehow, a moment of inspiration was had in discussing “risking your income to improve your turn’s outcome”, or effectively, “Betting”. At first, I was… hesitant. We already tried making a game that revolved all around betting & it was a disaster. But, I was intrigued by the suggestion this time, because the options for how you could theoretically place a bet in this situation was very very limited. Here’s the general idea:

On the first turn you have, you have no way to utilize this idea. If you have earned ‘silk’ tokens on a previous turn & decided to not spend them… then you have built up currency that you can leverage toward a ‘bet’. How it would work is before your turn begins you are handed the Collaborative Tic-Tac-Toe board with a set scenario from the previous player (let’s say that they ended their turn with x1 silk still on the board). Now, before you take the opportunity to roll the dice, you could ‘bet’ whatever ‘silk’ tokens you’ve stocked up for this turn by adding them onto the Tic-Tac-Toe board before you roll the dice. They cannot be added in such a way that creates a Tic-Tac-Toe before you roll the dice, because that would guarantee a payout. They can only be added to the Tic-Tac-Toe board in spots that do not create the ‘line’ shape. This Greatly increases your odds of getting silk back on your turn… But then there’s the big questions! How much silk will I get? / Is it worth it?

To be honest, at first, I was concretely of the belief that it would not beneficial. I truly believed that a player would consistently put money down & not get it back, or break even at best. But then, as you can see in the chart I started to make above, that there are many variations on this… And so I called up my good ol’ friend excel & got to work trying to deduce all of the statistics behind this scenario! And Wowowowowow. I cannot believe what I learned! It turns out that there are exactly x46 scenarios for how the board might appear at the beginning of your turn, and incredible statistics behind how these scenarios might benefit you! Let’s Take a look at the differences:

First up, the most logical scenario… Starting a turn with “no silk” on the board.

What we see here in our chart for information (top to bottom):
•Silk on the Board before Rolling Dice = ‘0’
•No Spot on the Board is ‘Restricted’ for Betting (non-placeable = ‘0’)
•There’s x9 Locations you could Bet on
•The max bet’s you could make this turn are ‘6’
•The cost of the bets range from 0 (no bet) to ‘6’ (max bet)
•The Payout ranges from ‘-4’ (losing x4 silk on the bet) to +3 (x3 silk more than you started with).

This is… very clearly a worst case scenario once you see how the rest of this chart plays out, and i find it really interesting that my friend Walter pointed this problem out before we had the math on it. As a funny point in the conversation, this possibility was abolished by our first mechanics change notated earlier in this post! So anyway, what about if you start a turn with ‘1’ silk already on the board?

So, now our statistics begin to change… Where previously there was only one possibility, now we have three unique outcomes for how a turn might start with ‘x1’ silk on the board before the turn begins. Note: Silk appearing on the board is represented as a blue ‘o’, and empty spaces are represented by a green “•”

As you can see in our little charts underneath each ‘Tic-Tac-Toe’ board, the statistics for our betting scenarios have begun to change to reflect the new board state AND! Note very specifically that not every board state is created equal! Having a silk token appear in the middle slot of the board is actually slightly more advantageous for a player than it is to have it on the corner or on the wall of the board (I find these statistics fascinating, and I am realizing as I am making this chart that there is now a very special learning curve available to players when taking on the challenge of interacting with these statistics!!).

Previously, we only had this set of options (in the last row of the chart):
•The Payout ranges from ‘-4’ (losing x4 silk on the bet) to +3 (x3 silk more than you started with).

Now, we have a span of options that ranges from:
•The Payout ranges from ‘-2’ (losing x2 silk on the bet) to +5 (x5 silk more than you started with).
to:
•The Payout ranges from ‘-3’ (losing x3 silk on the bet) to +4 (x4 silk more than you started with).

This is a crazy difference!! Let’s take a look at what happens to this chart when a player starts the turn with x2-silk on the board:

Wow!
Now we have 8-unique scenarios for how the statistics are playing out, and they are all over the place for how they are affecting the numbers we might experience! Note: Silk appearing on the board is represented as a blue ‘o’, empty spaces are represented by a green “•”, and now there is a new variable for positions where a player cannot place a bet, represented by a red “x”

(Also! A quick fascinating note: The featured image at the top of this post was from the first day we ever tried the ‘betting mechanic’, which was after I made this chart. This photo was taken because a player started their turn with ‘2-silk’ on #1 & #4 of the Tic-Tac-Toe board. The odds for this scenario are represented in the chart above, all the way on the left side. They placed ‘1’ silk on the board as their bet on position #5 (represented in red in the featured picture).. they then proceeded to roll the numbers: 3,6,9 on the 10-sided dice & got the MAXIMUM PAYOUT for this opportunity. It was concretely the moment I decided this mechanic had to stay for good).

If you take a good long moment to study this chart, you can see in the representation of the statistics that there is still always a risk associated with your betting… but the risk-reward relationship is actually getting better & better for a player as the number of silk starting on the board goes up in between each turn. When a player encounters a board with no silk, there is so much risk! But by this point in the chart, they are actually facing pretty minimal risk… being able to place up to 3-4 silk onto the board with a pretty minimal likelihood to lose everything you’ve invested is now surprisingly in the favor of the player!

While this may seem like a bad thing for the economics of the game, it is actually the exact opposite. promoting higher payouts for the players gives them much more agency in how they interact with the market & by taking huge risks they are offering up scenarios that pay out higher to their competitors sometimes… Let’s take a peek at the ‘3-silk’ on the board scenarios before talking about the statistics more:

Woah. So many options… Too many options?

Now it might be starting to get a little bit more difficult to even read this chart, because there’s so much data going on. At first we had 1-scenario, then 3-scenarios, then 8-scenarios, now 13! And, now something very significant has started to appear in the statistics… a very wild… potentially disastrous reality for the idea of this being a ‘betting’ mechanic that can be considered ‘balanced’?

Think about the decay… so far in our journey, the statistics have been ever more in the favor of the player whose turn it is when the data set hits them, from:

•The Payout ranges from ‘-4‘ (losing x4 silk on the bet) to +3 (x3 silk more than you started with).
to:
•The Payout ranges from ‘-3‘ (losing x3 silk on the bet) to +4 (x4 silk more than you started with).
to:
•The Payout ranges from ‘-2‘ (losing x2 silk on the bet) to +5 (x5 silk more than you started with).
to:
•The Payout ranges from ‘-1‘ (losing x1 silk on the bet) to +6 (x6 silk more than you started with).
to:
•The Payout ranges from ‘-0‘ (losing no silk on the bet) to +6 (x6 silk more than you started with).

We are now officially in a position where a player can take risks with literally a break-even penalty as a guarantee…. This is not how betting is supposed to work! We cannot have players knowing that they can bet all willy-nilly with no consequences!?!?

…. Or can we?
See…. there’s actually something truly magical about how the logistics of this play out within the relationship of the game’s mechanics. As we rise the ranks of ‘How much Silk’ is on the board before a player’s turn, the likelihood of this scenario actually taking place goes down significantly (because players will strive as hard as they can to get this silk off of the table during their turn). This is all to say, that the imposed rewards actually promote risk, which in turn, reduces the threshold of how much players can get away with so long as they are always keeping each other in check. (It is a cruel but beautiful system)… and we aren’t even at the end of the chart yet!

As we get to this moment in the chart, I am going to reveal that we have hit the peak of the bell-curve. There can be no more options at one time than what you see here… and the decay of options is going to go down at a rampant rate from here.

…. but now we hit genuine statistical magic. ~and listen closely friends… because I am going to teach you a trick about this game now if you have taken the time to read through all this math garbage! If a player starts their turn with x4-silk or 5-silk on the board before they roll the dice… it is a guaranteed statistically favorable outcome to bet (you’ll never encounter this in a casino I promise).

Now, granted, it is going to be EXTREMELY unlikely for you to encounter this scenario in the game. But, if you are like me, and you consider yourself to have no luck… let this be my gift to you my friend! This mechanic literally has the power to grant breakeven-guaranteed success… and it sounds terrible, but I promise you that it is lots of fun… not only for you to play with, but to watch other people play with as well. And, going way back to the top of this page, you will find that bringing more fun to the turn was the whole purpose to editing this mechanic.

Now for the craziest outcomes in the game:

Up until now, our chart has gotten bigger & bigger, with crazy vast possibilities…. but now, as the board gets more and more cluttered, the possibilities decay. The likelihood of a player every encountering this scenario is extremely low… it is very very atypical to somehow inherit the gift of x5-silk on the board before you roll the dice, but it can happen!

However, one of the ironies of the betting mechanic is that as we get to this place on the chart, it becomes every more unlikely that you can even place a bet on the board. of the five situations shown above, there are only two places a piece of silk can be placed as a bet…. and this decay has one last step it can make before being frozen entirely:

By some miracle of numbers, we have now spanned the vast gap from Alpha to Omega. Where this chart started with only one possibility of nothingness, there is ironically also only exactly one possibility of… fullness?

As an interesting point of fact, there is no way to have six items on a Tic-Tac-Toe board in any other orientation than this… and as an additional point of fact, there is no way to have seven or more items on a Tic-Tac-Toe board without forming a line.

And while this was an absolute mouthful of narrative to explain one… fairly simple idea, I found it absolutely necessary to do this math study before giving this mechanic the green light to be a part of our game. I wanted to study and truly understand this crazy idea, and after doing the research, I simply had to come here and share the results with you as well. This might very well be one of the best entries of the Librarium Games Design Journal that has ever existed in terms of logically explaining the machine inside the game (it’s not always the case that the math is literally beautiful to look at & fun to play with).

We have now played with this mechanic every single time that we have play tested Royal Threadcount… and it is a blast. It is so much fun to interact with, and it is an absolutely wonderful way to flesh out the unique and brilliant idea of the collaborative Tic-Tac-Toe mechanic. I hope that you found value & learned something from this crazy ramble today, and please stay tuned for more exciting journeys in the Librarium Games Design Journal! We still have so far to go to make this game real, but it is becoming more exciting all the time! And as always, thank you for reading!