Board Games are Totally Math! : Star Realms

Welcome to a long overdue edition of Board Games are Totally Math! Today I want to look at the numbers behind Star Realms., a two-player deck builder about building up your fleet of space stations and ships until you are strong enough to wipe out your opponent before they do the same to you. Currently sitting at a handsome 70th in the BGG board game list, this tiny box is a good contender for best ratio of quality design to expense.

So let’s head to the engineering section, and see how numbers power these beautiful star ships.


Fleet Building

Star Realms is undoubtedly a deck builder. You start with a weak deck, drawing trade ships and basic fighters. By the end you are throwing down huge warships and planet sized bases. It’s a great feeling, building your forces to that point, and is the practical definition of deck or pool building. But what is going on mathematically when we build a deck. Well quite simply, it is odds manipulation.

When you start a game, you have zero chance of doing any considerable damage, the most you can hope for combat wise is to draw two vipers for two damage. As you build your deck, you stack the odds in your favour to draw out more useful cards on any given turn. You could stack the deck with high damage cards, or carefully buy cards from a faction or with certain properties so that you have the best chance of pulling off devastating chains or combos.

I recently introduced a friend to Star Realms as he had had a bad experience with his first deck builder play through. His game club had asked him to play the Resident Evil deck builder and from the sounds of it, did a bad job of explaining how the concept of deck building worked. He asked them “Why do I have to get rid of my bullets, aren’t bullets useful?” and his teachers responded “You just do.”

A better response would be to say that you are stacking the odds in your favour. When you can only draw five cards on your turn like in Star Realms, every Scout or Viper is a waste of space that could potentially be filled by something far better. Literally anything in the Star Realms deck is better to draw than the starting cards. So building your deck comes down to adding strong ships, weeding out the weak, and planning what you add so that they work best together.

Warring Factions in the stars. One might call it star… wars

One of the fun elements of the building of your deck is the factions. I have known people perfectly well buying ships from any old faction, but the factions are each tailored to differing strengths and weaknesses, thereby helping you to easily steer your deck towards attributes that match your tactics or play style. I think looking at the factions and their individual cards is going to yield the most interesting statistical analysis. But before we get to that, I want to indulge try something else. From a number of plays before I started looking at averages, I formed opinions on the factions from how it felt to use them.

This is, as unbiased by hindsight as I can manage. My pre-statistical thoughts on the factions. How will they compare to my conclusions after looking at the numbers.

  • Blob

A blunt implement. I got the impression that the Blob were intended to be an all-out attacking force, few special powers, lots of ally bonus combat, simply a swarm of attacking mindless creatures. In some ways the theming of this faction is just right, a very alien race that attacks in force and in numbers

  • Trade Federation

Well it’s right there in the name. They are good at trade. I felt like they were good for spending power, healing damage and offering good defence from their bases. Maybe a good starting faction so you can spend big on ships, but weak in combat for the end game. Most of their combat seems to come from scrapping cards.

  • Machine Cult

Great for scrapping cards. Good combat strength and some useful unusual powers. I felt like these cards were ones to pick the odd few from, just to be able to scrap the weaker cards, but with some good combat uses

  • Star Empire

Close to Blob for cheapest faction. Not very high powered in combat, but with a lot of ability to draw extra cards making it a great faction for pulling off big chains.

So how did I do?

I will put up my spreadsheet of the factions with averages and totals of all kinds of things. You can find it here.

What do the stats say about the factions, how close was I in my initial thoughts?



With cards having an average base combat value of 3.55 and a total of 71 combat across the faction, plus an extra 0.7 combat on average per card if there is an ally present. The Blob blows the other factions out of the water in terms of raw attack power. In cost, they are the cheapest overall in terms of average expense per card. They have the most 1 and 2 cost cards of all factions. The stats back up the idea of them being a swarming, horde or a faction. They have 8 cards that offer draw card abilities, but 6 of them require an ally. But in fact their combat from ally powers is actually the joint lowest with two other factions, with Star Empire having the most ally combat. Although they certainly do work together better than any other faction. Only 4 Blob cards have no ally power, lower than the others with 7 or 6.

One thing I did not pick up on is that their scrap abilities tend to favour trade, which, with their low cost, suggests to me that the Blob is intended as an early faction to be scrapped in favour of others later on since scrapping cards for trade would be less useful in the end game.

Trade Federation

Well no surprise the Trade Federation are good for making money. A total of 31 trade is on offer from the blue faction, meaning you may be fighting over them if you want to afford the big ships. As for healing (increasing authority) they aren’t just good. They are the only option available. Without Trade Fed ships, your authority can only go down.

I said it felt like they have good defensive bases. Which I am not so sure of, it is a balance really. They are far better than the blob with the lowest shield total and no outposts. Yet in terms of blocking power, the machine cult and Star Empire have a little more total shield strength than the Trade Feds and the two have only out outpost between them, meaning opposition cannot bypass the bases to deal direct damage. The Trade Feds have 4 outposts of the 7 bases on offer. Perhaps what makes the Trade Fed bases feel so good in defence is their heal abilities.

I think it is somewhat inaccurate to say most of their combat comes from scrapping. In reality, scrapping accounts for about a third of their available combat. With the right ships, there is some damage to be done, but in reality, they do not look like a strong endgame faction.

Machine Cult

Sure these guys are the scrap faction. In fact apart from two blob ships, there is nowhere else to go to scrap you cards. If you want to lose those weak starting cards, better get some reds. I felt like they had the most unusual powers, but really they have the least cards with unique powers. Only the stealth needle and mech world had powers I couldn’t otherwise fit onto my chart. And though they have the second lowest combat potential. There is some decent strength there, which in combination with their other abilities, makes the Machine Cult worth considering for the attack minded player.

Star Empire

I feel like I was way off here. Although they do have a number of cheap ships. They are not far off the average cost per ship, and in truth, they have the fewest 1 and 2 cost ships. Saying they were fairly weak Is inaccurate, in fact they have the second highest combat total, and this, paired with the abundance of draw card abilities, means they can be a formidable force in combat terms. The average base combat across all purchase cards is about 2.2. This means that effectively, whatever is in your deck, you can think of a draw 1 card ability on a ship as being worth 2.2 extra combat over time, in addition to any other benefits the drawn card might end up having. A strong ability, and why Star Empire are probably my favourite faction.

Another thing I didn’t mention is the ability to make your opponent discard a card. Only the Star Empire has this ability, and with enough of them in your deck, you can pretty much have your opponent playing with a permanent handicap of only drawing 4 cards per turn.

So there we go. Just a short one for Star Realms. As you can see from the length of time since the last article, I am struggling for time to make these. That and Star Realms didn’t turn out to have much in the way of statistically measureable gameplay. So much of the powers on these cards does not translate into number form very well.

But still, we can see from the spreadsheet some of the intention in the faction system. On the one hand, you want a bunch of the same faction in your deck to make the most use of the faction powers, but on the other, you cannot get all you need from one faction. I would suggest a balanced diet. Something like a food pyramid. With the factions that match your chosen tactic at the base, and a few cards from the others to get the abilities you need that your main factions cannot provide.

Trying to pin down the probabilities on a game that by definition has you, the player, manipulating and changing the odds constantly was perhaps an ambitious task. I thought about plotting a cost to power output graph as a whole and for each faction to see which cards but I think any value I placed on the differing powers would be arbitrary and not very informative. Then there is the fact that the currency in this game is somewhat volatile. There is no saving up for something better. You simply spend all the money you have available on that turn or you lose it. You can buy the explorers as a kind of savings plan but they are not a reliable way to save and you may never get the money back you put into them.

As always. Thanks for reading. I am working to do better so by all means let me know if something needs improving. I don’t feel this was as great as the previous articles I wrote, perhaps I should chose my subject better next time. On that note, any suggestions for games I should are appreciated. Next I might take a look at Pandemic the Cure. I have been playing this a ton recently and the probability of the dice rolls is key to how the game plays and how balanced it is. Click subscribe for a good chance of seeing Pandemic the Cure broken down, tabulated and analysed, and hopefully other games too at a much accelerated rate.


Board Games are Totally Math! Forbidden Island

Welcome to Board Games are Totally Math! This series of will be an exercise in game design analysis for myself, and hopefully interesting for others. Board games are great to pick apart as a student of game design as the mechanics are all out there for you to see, and with the right mind-set you can work out all the probabilities and calculations that make a game work, and that is exactly what I intend to do.


Today I am looking at Forbidden Island. This game by Matt Leacock is a firm favourite of mine and has cemented itself in my house as a go-to couple game. It’s a game about uncovering treasures from a mystical island as it sinks beneath your feet. You really get the feeling playing this game that the land is sinking beneath you, it delivers on that “Oh my god we are all going to die” panic feeling that co-op games do so well, and it gives you a great sense of relief and accomplishment when you succeed. That is all thanks to the Leacock’s excellent design, so let’s pick it apart and see how he did it.


I will assume some familiarity with the game in these articles, so feel free to watch a video rule guide, read the rules or play a game before continuing if you need to.


That sinking feeling

Forbidden Island features a simple yet smart system for handling the automated actions of the island as it sinks. This is key to the tension of the game. The mechanics make it clear from the start, the island will sink and you cannot stop it. All the players can do is delay the sinking long enough to get the loot and escape.

Maybe you think, surely there is a way to play well enough to save everything. Well no. look at the initial set up, six tiles are flooded to start with, the first player could if perfectly positioned shore up three of those tiles, and if the right cards were dealt then players could shore up another two with sandbag cards, but that still leaves one vulnerable tile, a tile that could be sunk at the flood phase of the first turn if a waters rise card is dealt. Only the engineer character has any chance of keeping all tiles 100% safe. To me the message to the player is clear, prioritise what you need to secure and hope that what sinks is something that won’t hurt you too badly.

The entire gameplay is centred on the player’s decision making of what to save and what to sacrifice, so how do the numbers achieve this? There are 24 island tiles, one (Fool’s Landing) which players must protect at all cost, and four pairs of treasure tiles which can end the game if both of one pair are lost. Also there may be tiles needed to easily traverse the island, though not essential, they can make things harder if lost.

At the start if the game, players can feel pretty safe, after all, when a flood card is drawn you have a fairly low probability of flooding or sinking a necessary card (7 in 24, not bad right). But the game actively adjusts the odds in your favour. Maybe you lose a tile, that card is removed from the flood deck, the chances of getting a card you don’t want are now higher (now 7 in 23 chance of losing something important, lose another one and it’s 7 in 22, and so on). Players can see the island getting smaller and smaller, reinforcing the fact that you really ought to shore up those essential tiles.


Not what we had hoped for

There is an ebb and flow (no pun intended) to the management of tiles. When a tile is lost, then there is an increase in the odds of the next tile to go being something you sorely need. On the other hand, there are times when you can turn the odds in your favour, when you locate a treasure, suddenly the two tiles you needed for it are fair game to be allowed to sink, or maybe players identify an area that is not needed for traversal and can be abandoned. Sure this concentrates dangerous cards in the flood deck, but it can be used to get a respite and concentrate on the tiles you need the most.


Treasure Hunting

For me, getting a full set of treasures is one of the trickiest aspects of the game. It is affected strongly by the player count and the hand limit of five cards.

Getting the set of four matching treasures would be easy, except for the hand limit. Since you can only have only have five cards in your hand at any one point, it leads to agonising decisions on what to discard when you have too many. This is where the rule in the book that allows you to look through the discards becomes useful. Discard one treasure card from a set, and you can still complete it by the time the treasure deck runs out, discard a second treasure from that deck, and you will need to go through the deck again to complete the set. Or perhaps you decide to discard a sandbag or helicopter, you have to think, would that be more useful later on? Might I need the sandbag to save a tile? Will I find another helicopter to escape the island before it sinks?

This decision making, in my opinion only gets harder with more players. It takes up a lot of actions to pass cards to other players, and who gets what card from the deck is an area where luck can really make a difference.

Regardless of good or bad luck, to win the game, you are usually going to need to go through the treasure deck at least twice. Maybe the first trip through the deck you get one or two full sets, but you would need immense luck and co-ordination to acquire all four sets on the first pass, inevitably you will come to a point here you need to discard more than one of a certain set and thus, need to make a second trip through the deck inevitable. Which leads me to the next topic.


Escape in the nick of time

Generally, the game always provides a tight finish, where you are running around to grab the last treasure and leave the island as the last few pieces are disappearing. If that doesn’t happen, our usual response is to play again on a higher difficulty. I would definitely recommend playing the harder levels as you get familiar with the game. The easiest level is a tutorial really, it’s no challenge for an experienced group.

So how does the game balance the ending? Even with an easy win, the island is crumbling around you as you flee. Well the trick is in the design of the treasure deck. Since you will most likely need to go through the deck twice, possibly a third time for that last elusive card, it means you will draw the three waters rise cards twice at least. Now take a look at the water level marker. Starting on the easiest setting there are nine marks above it, so once the third waters rise card appears from the third run through the deck, the players lose the game. On the highest difficulty, the game must be completed before the final waters rise card is drawn from the second pass through the deck.


One more and we are doomed

It is good that the completion of the treasure collecting should coincide with the game over point on the water tracker. It puts a natural turn limit on the game meaning you can’t just hang around forever, it also mean that by the time you have all or most of the treasure cards you need, the water marker is so high that you are drawing five flood cards and sinking tiles all over the place.


Gameplay tip

The deck is designed to end the game one way or another sometime between the end of the second run through the deck and the end of the third, depending on difficulty level. We know how long the first run through the deck will last, there are 28 cards and each player gets two to start with and two at the end of each turn, so the first deck will last between 10 and 12 turns depending on player count.

Turns = (28 – (2 x player count)) / 2

But the subsequent passes through the deck are not so predictable. Depending on how many cards are still held by players, the treasure deck can be very short in deed, this is more noticeable as the player count rises. The fewer cards discarded, the smaller the deck will be when shuffled, but there will still be three waters rise cards in there. So the tip I would advise, play aggressively, get those treasures collected and cashed in before the first deck runs out. The more you can discard before the shuffle, the longer you will get before the waters rise cards end the game.


Player count

I’ve touched on this already, but maybe there is more to be said. I mentioned before this is a favourite couple game for me and my girlfriend. It just works well with two, there is less to worry about with card sets being distributed over multiple players. With two, you can pretty much aim to complete one set each on the first run through the treasure deck and then one more each to finish the game. And when the treasure cards are dealt, there is a 50/50 chance that the cards you need will fall to you and not your partner. Yet with more players, you can end up with cards all over the place, a lot more actions are expended trying to get cards to the right person.

Sure it is extra challenge, which can be great, but seeing as a lot of our gaming friends are quite casual, it just means the game is a little too weighty at times for our group with higher player counts. But being objective, I do look at the mechanics and think this is a vastly harder game with three and especially four players. There are a number of mechanics that escalate the difficulty rapidly.

  1. Smaller treasure deck – With more people holding cards, you will run through the deck quicker and hit waters rising cards more frequently.
  2. More dispersal of treasure cards – Be prepared to do a lot of card trading
  3. Longer downtime – If you have the full set of the final treasure and you cannot make it to the right tile on your turn, then everyone has much longer to keep things afloat before you can claim the treasure.

Gameplay Tip

The only real advantage in more players is that you have access to more player abilities and can spread the treasure card sets out between more people. MAKE SURE YOU MAKE USE OF THIS. Funnily we often joke how useless the navigator and messenger are, but in higher player counts they have more use, especially the messenger. The messenger doesn’t even need to go for full sets of treasures, they can use their ability to distribute all of their cards to those who need them the most.


I hope that gave an insight to this elegantly designed game. This was I think a gentle with which to start this series. Not very maths intensive, as I said the probabilities change on the fly throughout the game so much it would be pointless to quantify them.

As always, share your thoughts below, and like and subscribe if you want to see more like this. I am considering a few games from my collection or that I am familiar enough with to try next. Front runners for the next edition of board games are totally math are Ticket to Ride, Star Realms, Alhambra or Patchwork. Good scope for some statistical analysis there. Suggestions are welcome for future games to pick apart.

Thanks for reading.

BGG 24 hours game contest – May 2015 – Knight at the Inn

Follow the links below for the components and rules to my 24 hour game contest entry for May 2015. If you want to know about my journey in board games so far and the development of this game, then read on.

Knight at the Inn Components

Knight at the Inn Rule Book

Getting into Board Gaming

As an aspiring game designer, I have really enjoyed diving head first into the world of board games, or more specifically the side of board games known as designer games or hobby games. I have enjoyed a lot of games over the years (although even back then I had to have my arm twisted to play Monopoly or Cluedo). I guess it was inevitable that once I had a taste of games beyond the mass market stuff found in high street toy shops, I would get hooked.

For me the game that started it was Talisman, I got myself invited to a game and had a blast, it was an experience like the western RPG videogames I enjoy but on cardboard. I began learning all I could about the hobby and before I knew it I was through the looking glass, down the rabbit hole, in at the deep end and all the other clichés for getting deeply involved in something. After that my collection began to rapidly grow, I converted my girlfriend Gemma into a board-gamer as well and we have not looked back.

I think one of the things I like most about the hobby is transparency of the design in the final product. If you know where to look, there is every little obstructing the player from the designers decisions. The rules and all the components are all there for you to see and analyse in the box. And as a game designer I can’t help but try to deconstruct every element; why that number of cards? Why is that action worth that many points? Why are those dice results special and not another combination? Which makes it all the more impressive when it all comes together to make an interesting, well balanced and fun game. So having established that I have been suitably inspired, it’s my turn…

BoardGameGeek May 2015 24 hour game contest

– My Entry – Knight at the Inn

Playing Knight at the Inn

Playing Knight at the Inn

I had attempted a game or two before, and have had dozens of designs in my head. But never had I gotten past the prototype phase. So the 24 hour contest was looking like it would be a great challenge and a good incentive to get over that hump. I was a little unhappy with the theme being “Knight” I was struggling to come up with a concept that didn’t revolve around killing things with swords (I don’t like to go for the obvious choice). Inspiration struck thinking about chess pieces and knights marching across a medieval countryside. What formed in my mind was an abstract strategy game about knights returning home and staying the night at inns along the road home. And being a big Game of Thrones fan, I thought about the way that main characters traveling across the land would always end up in the same tavern.

I quickly put together a pen and paper prototype and tried It out with Gemma. I wanted it to be a tactical game of maneuvering your knights across the board whilst blocking your opponent. So I made sure there was limited space at the inns for tactical blocking and covering of pieces. And I tried to give the pieces variable abilities to allow them differing roles in gameplay for players to discover. The lone knight as an easy to move but vulnerable pieces ideal for dashing about and pinning threatening opponent pieces, the King is a difficult to move piece but can be a strong tool to muscle your way though and block pieces.

After the first play though, we realised we had had a great time. Sure new rules were implemented on the fly but it was fun, we could see clearly where we could move, who we could block, where would leave us exposed. The tension seemed to really build towards the end, just when you thought you had a handle on it and could run away with it, your opponent would get a foot hold. A happy accident of the design, that as you got more pieces to the end space, you became more vulnerable to being pinned down or blocked. Most games we have played seemed to come down to the last few pieces. I felt I was onto something good when after one play, we immediately wanted to set it up again and go another round.

Development we pretty well but I made a mistake of starting my project a few hours before I had to be in bed for work early the next day.I spent about 4 hours setting up the basic rule book and pieces before I had to call it a night. I may not have stuck strictly too the rules, but three days later all I needed to do was make some pretty pictures for the pieces and finish up the rules before making my final presentation.

Going Forward

I have had a bunch of plays of this game with Gemma. But I think the next step would definitely be to have some others play it. See whether it merits further development, I have my concerns about it and things that I like, but it’s hard to say what direction I should be taking those elements right now. So far I haven’t gotten much feedback form other people, so I will have to start going after play testers some more. That or I will just move onto the next project. One thing I know is that the rules need a little clean up.

The Game Tinkerer – King of Tokyo AI Opponents

The Game Tinkerer – Because no game is ever finished

This is the first in a series of articles I have been meaning to write about modifying games. Be it video games or board games, sometimes the base game is just not enough. It could be a good game I want more of, or a bad game that needs fixing, or just using the constraints of the game to stretch it as far as it will go. I hope to make a few of these articles, covering topics such as house rules, alternate ways to play, video game challenge runs and maybe some game mods.

House Rules – King of Tokyo AI opponents

Today I will be outlining the AI rules I use in King of Tokyo when I want more people to play against. Great if you want a solo variant or just more monsters to fight against.

Hamsters don't make good opponents, they can't sit still long enough

Hamsters don’t make good opponents, they can’t sit still long enough

I have had King of Tokyo for some time now but have struggled to get it out to play with more than three people. Trouble is, as great as this game is, it get better the more people you have. Sure you can pull it out for a party or a gaming meet up but the rest of the week if you live alone or with your partner (like me), it is gonna stay on the shelf. So I developed a way to play against automated opponents. With some simple rules you can have games against some fairly competitive AI players. I have used these rules to play solo and with my girlfriend in three and four player matches and had a good time.

As deep as King of Tokyo is, essentially you only have a few decisions to make; which dice to keep and which to re-roll, whether or not to buy that card you can afford, and whether or not to yield Tokyo when attacked. My rules randomly determine each of these decisions in a way that feels like playing a human opponent, a slightly dumb, very aggressive human, but any more complex and it would be a pain to implement.

AI rules

Rolling and Re-Rolling the Dice

The dice are, despite the re-rolling mechanic, a very random element of this game, so the following rule set will usually simulate a convincing imitation of a human players dice choices.

Each of the three rolls work in much the same way. Rolling the dice, determining the “useless” dice for re-rolling and keeping the good dice. I class the dice faces are numbers and symbols (heart, energy or attack)

“Useless” dice are defined:

  • Any symbols that cannot be used, for example an AI monster will discard hearts if it has full health or cannot attack or collect energy.
  • Any numbers that are impossible to get three of a kind with. e.g. There are two threes but the other dice are already being kept for another purpose.
  • Any single number not repeated (the AI monster doesn’t take risks)
  • Any pair of numbers of lower value than another pair.
  • Attack symbols when the monster is below 4 health and outside of Tokyo

Using this method the AI will generally collect energy, attack monsters, heal when necessary, play less aggressively when near death and try for victory points when a pair or triple is number is rolled.

Buying Cards

Check the number of energy cubes the AI has, if it is enough to buy a card, roll a dice to decide whether or not to purchase it.

If the monster can only afford one card, role a dice, if it lands on an energy or attack symbol buy that card. If more than one card can be bought, do the following:

  1. Role a dice until you get a number, going from left to right (or top to bootom, however you have your three cards arranged) the number on the dice is the starting card.
  2. If the monster can afford the card, roll a dice the same as rolling to buy a single card, otherwise, skip to the next card.
  3. Carry on in this fashion until all cards are bought or skipped, if a new card comes out which the monster can buy, roll for it at the end.
  4. If the monster can afford all three but buys none, it is considdered that it does not want any, in that case, providing it has 5 energy or more, pay 2 energy to scrap cards and draw new ones. Roll to buy any new cards as normal.

Yielding Tokyo

AI monsters will yield Tokyo or not according to their health

8 or more Do not Yield Tokyo.

7 – 5 Roll one dice, if it is a symbol, yield Tokyo.

4 Roll one dice, only stay in Tokyo if it is an attack.

3 or less Yield Tokyo

Using Cards

Some cards can be used at times of the players choice, so assume that the AI monster bought the card to use it. The AI should choose to use card abilities at any point that benefits them, messed with someone else, and won’t hinder themselves.

Golden Rule

The AI will do anything that a human trying to win the game would obviously do.

For example, I played a game where all monsters had 3 or less health, and the AI monsters kept trying to buy a card that would deal 3 damage to all monsters thus ending the game without a winner. I didn’t allow it, sure there would be some sadistic player who might find it fun to screw the game like this but it is not something I would encourage.

Also the AI are trying to win, so if there is a card they can afford that would win the game for them, they should buy it at the first opportunity without rolling the dice. It’s not fun to have to make yourself lose like this, in fact I have made the AI ignore the cards in situations like these and gone on to won, but I know deep down that I lost, I just wanted to play a little more.

So there it is. Give it a go. Feel free to comment if you enjoyed the rules or had any suggestions to make the rules better.