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.


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