97% Of Catan Players Choose Wrong
Original Script:
Focus
Learning all the numbers and statistics of Catan, and how it can help your gameplay.
T/T
How to win with MATH in Catan
Catan Math for Beginners
My math teacher plays Catan
When your math teacher plays Catan
16.6% chance of being robbed.
These numbers will change how you play Catan.
Attention Ideas
Stop giving me statistics and tell me what to do!
Loading bar with diff % to visualise difference in pips
Notes & Ideas
19 resource cards
25 dev cards, etc
# of hex tiles
Pip probability
How many ways are there to get 10 VPs?
Static vs variable points
Income / production chart
When do the 5 resources you put into getting a city pay off? VS expansion.
Odds of other players hitting certain resource goals and how to respond to that
Calling out trade value based on the pip of each resource
Now suppose your settlement is on a 6/4/11 intersection (which corresponds to dots •••••/•••/••, or as I will write from here onward, 5-3-2). Then the chance that this settlement will pay off is 5/36 + 3/36 + 2/36 = 10/36. It’s reasonable to assume that in an average game of Catan, there are 72 rolls. Meaning you should expect 20 of these resources through a game.
https://divisbyzero.com/2010/01/06/playing-the-probabilities-in-settlers-of-catan/
https://developingcatan.files.wordpress.com/2011/02/settlers-of-catan-analysis.pdf
If this is how many resources you can estimate you will get, how does that affect your strategy? Should you be battling for longest road if you don’t have the placements for it, and the same for knights? Should you focus more on expansion vs cities? Will your 2:1 port give you enough cards in return?
https://cs.stanford.edu/people/nick/settlers/DiceOddsSettlers.html
https://acalanesblueprint.com/wp-content/uploads/2020/05/Grand-Strategy-in-Catan-1.pdf
Order
Hexes on board, their value
Pips on hexes, their value
Avg # of rolls in a game
What you can expect to build with those resources, and your opponent
How many VPs you need and how many ways to get them
Resource cost to win each way
Static vs variable points
Income production over time, when do cities/settlements pay for themselves?
How many resources away from victory, and what are they? Same for opponents.
Script
(rewind) Math + Strat = Path to Victory
(hook) What if I told you that you could solve your Catan problems with some basic math? Would you take the blue pill and go back to trying to get lucky, or take the red pill and see just how deep the catan board goes?
(hook) You’re playing a board game, you don’t want to do math, this is such a dumb video idea, why are you still here? My guess is, you can sense it, you know that there is something to be learned here that could very well change the way you think about Catan. And you don’t even need a calculator (hopefully).
Let’s start with the easy stuff.
Script v2
If you picked the absolute best possible initial placements in Catan (which is basically impossible), you would still only have a 50% chance of getting
The best chance you have to get resources with any given dice roll is 50% if you pick the best two initial placements on the board. And that is a perfect scenario and the number is only 50%. This should get you thinking of two things; 1) you shouldn’t feel too bad when your rolls don’t come up and 2) what can you do to pump up those numbers?
Let’s face reality for a second. To get a 50% you would need a insanely lucky board state, where the 6/8/5 and 9 all huddle around each other AND you are playing with incredibly stupid opponents. Which is all to say, it’s not happening. On the opposite end of the spectrum, if you picked the absolute worst spots, ignoring the desert, you would have a 16.6% chance of getting a resource each roll. If we take the average of best and worst possible outcomes, you get 33.3% chance of a resource each roll. That should be your NEW worst case scenario. From now you, you are aiming to as high up from that number as possible.
6/8/5/9 = 18/36
6/8/5/9/4 = 21/36
4/5/6, 8/9/10 = 24/36
https://catan.bunge.io/
Script v3
You have a 66% chance of getting a resource with every dice roll if you place your 2 initial settlements on 4,5,6 and 8,9,10, in whatever combination you prefer. That is a HUGE percentage. We know this because these pips represent the odds of that number being rolled, you see these 3 dots on the 4? It means that out of the 36 total possible combinations of rolling two 6-sided die, only 3 combinations can add up to 4. But.. if you take the total pips of these first two placements, 24 out of the 36 possibilities are in your favor. Placing on these settlements will have you rolling in resources and conquering catan. Okay, that’s it, you are a Catan master now, wait, you want more? If you insist, now what if you changed up those numbers and focused on the highest pips. In that case you would take 5/6/8 and 9. And if you magically get onto these numbers, you only have a 50% chance of getting a resource every roll which is a lot lower however, the probability of each individual number is not equal. You have a 11.11% chance of rolling a 5, but only a 8.33% of rolling a 4. So if 5 comes up 3% more often, as it should, you would be getting twice as many resources from that dice roll.
In an average game of Catan, there are about 72 dice rolls. I don’t have data for that number, but my gut tells me it’s close enough AND it’s a convenient number to do the useful math we want to do. Now if there are 72 dice rolls in a game, then according to this probability graph, these are the numbers you will get and therefore is a good guess of how many of each resource you will get throughout the game from those two initial placements. Here’s a list of how many of each resource you would get based off these pips in a 72 dice roll game. So with those perfect placemats, you can expect X wheat, X ore, X sheep, X wood and X brick. Seeing what’s in front of you, can you guesstimate if this is enough to win? If you build all your settlements (5) are cities (4), with minimal roads, you will need to spend, 6 wood, 6 brick, 3 sheep, 11 wheat, and 12 ore for 9 points. It’s no surprise that wheat is the most important resource and you better damn have placed on a strong wheat or go revisit this video.
Okay great, you have a ton of resources coming in, you are holding like 14 cards in your hand because you are just that loaded and a 7 is rolled. Congratulations you got all those cards for nothing. If you don’t want to be the biggest loser, get it cause you lost a lot of cards, you can’t just settle for the numbers, you have to also consider resource synergy so you can spend the resources. Your wood and brick numbers should be on par, as well as your wheat and ore numbers. Other every dice roll, you have a 16.6% chance of 7 being rolled and you losing half the cards in your hand. Assuming you have more than 7 in hand. And if you do have that many cards, there’s a good chance you are doing well in the game are likely gonna be blocked or stolen from, in which case you better have some knights handy.
Dev cards
If I had to break it down into one sentence, number variety with best total number of pips with a strong wheat is the way to go.
Now is it better to double down on the same numbers for higher income or diversify to have a more steady income? This is when you have to take a look at the board. If the city resources are in abundance, you might favor diversifying your numbers so that as you build cities and gain the attention of the robber, it isn’t that easy to slow down your overall production. But if city resources are scarce, you might want to have strong city resource numbers to ensure you are getting those city resources.
Script v4
You know why poker is better than Catan? Look right here (arrow). If Catan was like Poker, You see these little stats at the corner of the screen, these you’d have those little stats on the corner of the screen to let the audience know what the percent chance is for players to win with their hand. If Catan wants to be taken seriously as the spectator sport, it needs information like this for viewers and commentators. Oh sheep, blue has a 42% to get a brick if blue rolls a 4, then he can build that road and cut off red’s expansion options, that’s a bold move cotton, let’s see how it plays out. And this is what it would look like. I had the chance to do some live commentary of a Catan tournament recently, and I think it would be (hand gesture) this much more fun AND helpful to the audience and commentators to see those numbers. It would look something like this; Each player would be listed, with the resources in their hand. And, beside that, the % chance of them getting a particular resource to build something with the cards in their hands. rolling a particular number that would give them the resource needed to build a thing. And then if you were doing live commentary for an audience, you could be like, oh sheep, blue has a 42% to get a brick if blue rolls a 4, then he can build a road and cut off red’s expansion, that’s a bold move cotton, let’s see how it plays out this is a do or die roll for red ladies & gentlemen. Catan deserves to be a spectator sport, and this would be a huge step to making it more accessible as a viewer. And the learning opportunity for viewers? Holy sheep, it would be a game changer.
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If Catan Was Like Poker, It could be a huge spectator sport. And it would only take a few small tweaks. Look right here (arrow). You see these numbers? These percentages show the probabilities of Poker players winning their game. If Catan wants to be taken seriously as the spectator sport, it needs information like this for viewers and commentators. Oh sheep, blue has a 42% to get a brick if blue rolls a 4, then he can build that decisive road and cut off red’s expansion options, that’s a bold move cotton, let’s see how it plays out. If we used these in Catan, it would look something like this; Each player would be listed, with the resources in their hand. And, below that, the % chance of them getting that resource to build something with the cards in their hands. Catan deserves to be a spectator sport, and this would help it reach more people. “Oh sheep, Blue has a 12% chance to get a brick to build a road and completely destroy Red’s chances of expanding! That’s a bold move cotton, let’s see how it plays out.”
Poker Players around a table, cards are replaced with catan board. Cards in hand are replaced with resources. Crowd cheering noises.
Me in Circle. Draw attention to numbers.
Me & clone playing Catan. Me as a commentator with Cotton on side screen.
Break down how numbers are presented
That would be awesome for spectators, But how would these numbers help the players? They wouldn’t be allowed to see the odds and have to actually do the math for themselves, in their head. But I’m not going to make you do Math, love you all too much to have you suffer through that, so during the flop, we’ll go through some of I’m just going to tell you the most important numbers you need to know to get better at Catan and the most helpful tip happens at this time in the video. on the flop. And at the turn this time in the video, you’ll learn the golden rule that will let you see the odds during the game. completely change how you do placements in Catan. And the river will just be the cherry on top. Let’s get started.
Dice transition (catan dice)
Clone & I, point to numbers, gesture you can’t see them
Counting on fingers
Relief for not having to do math.
Most helpful time stamp
5 cards unflipped. Tip #3 is highlighted.
Show the flop as a timeline for video, back/front of card same as catan resources. brick/sheep/wood as flop, wheat is gold, ore is river
Flop shows %’s, 66% 11%, 8%, etc
This time in the video, clone points up
Golden rule type in front of clone, clone tries to peak around it.
Did you know that you have a 66% chance of getting a resource with every dice roll if you place your 2 initial settlements on 4,5,6 and 8,9,10, in whatever combination you prefer. Those numbers will give you the best chance to get a resource with every roll. As you know, these pips represent the odds of this number being rolled, you see these 3 dots on the 4? It means that out of the 36 total possible combinations of rolling two 6-sided die, only 3 combinations can add up to 4. But.. if you take the total pips of these first two placements, that means 24 out of the 36 possibilities are in your favor. And if you ignore 7 rolls, then that’s 24 out of 30 combinations. Placing on these pips will have you rolling in resources and conquering catan. Now what if you changed up those numbers and focused on just the highest pips. In that case you would take 5/6/8 and 9. And if you somehow manage to get onto these numbers, you would only have a 50% chance of getting a resource every roll, which is a lot lower, however, the probability of each individual number is not equal. You have a 11.11% chance of rolling a 5, but only a 8.33% of rolling a 4. So if 5 comes up 3% more often, as it should, you would be getting twice as many resources from that dice roll. The more diversified your numbers, the more steady your game will be. But, just like Poker, sometimes going all in on just a few numbers will can put you ahead of the pack.
Motion graphics, Me in circle, gesturing to the right.
I’m in circle for non-bold parts. I can do YT cuts liberally, don’t have to memorize.
Circle expands to full screen.
Me and clone. Clone puts on his Poker glasses.
Clone throws resources at camera.
Clone throwing resources in the air.
In an average game of Catan, there are about 72 dice rolls. I don’t have data for that number, but my gut tells me it’s close enough AND more importantly, which is perfect because it’s a convenient number to do the useful math we want to do. Convenient how? Because there are 36 possible combinations of rolling two 6-sided dice. If you assume that these pips indicate how many times 4 is rolled every 36 rolls, then doubling that will tell you how many times that number will come up in an average game. can double that pip count for 72 rolls and expect 4 to be rolled 6 times in an average game. Now if there are 72 dice rolls in a game, then according to this probability graph, these are the numbers you will get and therefore is a good guess of how many of each resource you will get throughout the game from those two initial placements. Check out this list. It shows you how many of each resource you should, on average, expect throughout a game from your initial settlements.
2/12 = 2 resources
3/11 = 4
4/10 = 6
5/9 = 8
6/8 = 10
https://www.alexcates.com/post/board-game-breakdown-settlers-of-catan-the-basics
Notice anything? Those numbers are double the pips. Which means with some quick math, you can easily guesstimate how many of each resource you will get with your initial placements. Pretty neat right? Please take a second to let that sink in so that you remember it for your next Catan game. This is the golden rule I promised earlier that will help you This is a really useful way to plan out your settlements more effectively. And while you are letting that sink in, make sure to drop a like & share this video with someone who could use this information. If you want more gold like this, don’t forget to like this video and share it with someone who could use this advice. So using a gameboard and placements from a previous video of where a Tournament Champion placed, you can expect X wheat, X ore, X sheep, X wood and X brick. Now seeing what’s in front of you, can you guesstimate if this is enough to win? If you build ALL your settlements (5) and cities (4), with minimal roads, you will need to spend, 6 wood, 6 brick, 3 sheep, 11 wheat, and 12 ore for 9 points. Knowing this, are you happy with your placements?
MG with circle
Pretty neat right? MG of clicking the Like button.
Please take a second. Full screen with clone. Clone analyzing pips.
Back to MG
Flop timeline, turn flips,
Clone and I, clone blocked by golden rule type.
Clone gives 2 thumbs up from behind the type.
Let’s say you place well, you have a ton of resources coming in, you are holding like 14 cards in your hand because you are just that loaded and a 7 is rolled. Congratulations you placed really well and got all those cards for nothing. There are only so many resources you will get throughout a game with 72 dice rolls, so losing that many resources on a 7 roll is a game losing scenario. If you don’t want to be the biggest loser, get it cause you lost a lot of cards, you can’t just settle for numbers, you have to also consider resource synergy so you can spend those resources. Your wood and brick numbers should be on par, as well as your wheat and ore numbers. Remember this, every dice roll, there is a 16.6% chance of a 7 being rolled and you losing half the cards in your hand. Assuming you have more than 7 cards. 16.6% is not only a really high number, but 7 is the highest probability outcome of any dice roll, and it’s basically guaranteed to happen at least once every 6 turns. So you better be able to spend at least every other turn. And if you are holding that many cards, there’s a good chance you are doing well enough in the game that you are going to be blocked pretty often, in which case you better have some knights handy.
Clone & I, clone is super happy with all his cards.
7 is rolled.
Clone Cries as he gives half to the bank.
Biggest loser comment, gets offended
I Block clone’s hex with a knight, offended.
MG
Clone offering cards to steal while I am about to steal one.
Which shouldn’t be too difficult because you have a 56% chance of drawing a knight card from the development card deck. There are 25 cards in the development card deck and it is broken down like this; 14 knights (56%), 5 victory points (20%), 2 road building’s (8%), 2 year of plenty’s and 2 monopoly’s.
MG with circle
Although you will be mostly getting knights. It’s still well worth the resources because if your 8 is blocked all game, those 10 resources you were expecting isn’t coming your way. 3 resources to defend 10 resources and slow down your opponents resource generation is well worth it.
MG with circle
If you are super eager to start up a game of Catan and use this information, you should first check out this video where a Catan champion shares his secrets about initial placements so that you have a 100% chance of being prepared for your next game.
Clone rolling dice. End card comes up. Clone gives to peak from behind..
Script V5
Filming notes:
Do the whole thing close up. Word for word, gesture for gesture, with hands in view (wide angle gopro).
THEN, do the clone version so the clone can listen to the edit and react well, mark where you would cut to the clone so you can gesture towards him.
Lots of closes up with big typography flying in
Mild camera shaking or zooming in, no static shots
Cut in to hide edits
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If Catan Was Like Poker, the game would be presented in a completely different way and make the already epic game of Catan nature of the game would be amplified making a huge spectator sport. And it would only take a few small tweaks. Look here (arrow). You see these numbers? These percentages show the probabilities of Poker players winning their game. If Catan wants to be taken seriously as the spectator sport, it needs information like this for viewers and commentators. Oh sheep, blue has a 42% to get a brick with this next roll, then he can build that decisive road and cut off red’s expansion options, that’s a bold move cotton, let’s see how it plays out. If we used these in Catan, it would look something like this; Each player would be listed, with the resources in their hand. And, below that, the % chance of them getting that resource. How cool would it be to see these numbers updated in real time? Each time a player places a settlement, their percentages rise. And you can see, with numbers, which players are dominating the board.
Anime lines, split screens, resource cards being flipped. 3 ores, 1 wheat and wheat revealed, player pop-offs, other player disappointed.
Poker Players around a table, cards are replaced with catan board. Cards in hand are replaced with resources. Crowd cheering noises.
Me in Circle. Draw attention to numbers.
Me & clone playing Catan. Me as a commentator with Cotton on side screen.
Break down how numbers are presented
Player places settlement, numbers adjust.
But how would these numbers help the players? They wouldn’t be allowed to see the odds and have to actually do the math for themselves, in their head. But I’m not going to make you do Math, I’m just going to tell you the most important numbers you need to know to get better at Catan and the MOST helpful advice happens at this time in the video.
Dice transition (catan dice)
Clone & I, point to numbers, gesture you can’t see them
Counting on fingers
Relief for not having to do math.
Most helpful time stamp
Did you know that you have a 66% chance of getting a resource with every dice roll if you place your 2 initial settlements on 4,5,6 and 8,9,10. As you know, these pips represent the odds of this number being rolled, you see these 3 dots on the 4? It means that out of the 36 total possible combinations of rolling two 6-sided die, only 3 combinations can add up to 4. And.. if you take the total pips of these first two placements, that means 24 out of the 36 possibilities are in your favor. And if you ignore 7 rolls, then that’s 24 out of 30 combinations. Insane odds, if you lost a game with those starting numbers, you might need to donate Catan to your local animal shelter because. Now what if you changed up those numbers and focused on just the highest pips. In that case you would take 5/6/8 and 9. And if you somehow manage to get onto these numbers, you would only have a 50% chance of getting a resource every roll, which is a lot lower, however, the probability of each individual number is not equal. You have a 11.11% chance of rolling a 5, but only a 8.33% of rolling a 4. So if 5 comes up 3% more often, as it should, you would be getting twice as many resources from that dice roll. The more diversified your numbers, the more steady your game will be. But, just like Poker, sometimes going all in on just a few numbers will can put you ahead of the pack.
Motion graphics, Me in circle, gesturing to the right.
I’m in circle for non-bold parts. I can do YT cuts liberally, don’t have to memorize.
Circle expands to full screen.
Me and clone. Clone puts on his Poker glasses.
Clone throws resources at camera.
In an average game of Catan, there are about 72 dice rolls., which is perfect because it’s a convenient number to do the useful math we want to do. Convenient how? Because there are 36 possible combinations of rolling two 6-sided dice. If you assume that these pips indicate how many times 4 is rolled every 36 rolls, then doubling that will tell you how many times that number will come up in an average game. Check out this list. It shows you how many of each resource you should, on average, expect throughout a game from your initial settlements.
2/12 = 2 resources
3/11 = 4
4/10 = 6
5/9 = 8
6/8 = 10
https://www.alexcates.com/post/board-game-breakdown-settlers-of-catan-the-basics
Notice anything? Those numbers are double the pips. Which means with some quick math, you can easily guesstimate how many of each resource you will get with your initial placements. Pretty neat right? Please take a second to let that sink in. This is a really useful way to plan out your settlements more effectively. So using a gameboard and placements from a previous video of where a Tournament Champion placed, you can expect X wheat, X ore, X sheep, X wood and X brick. Now seeing what’s in front of you, can you guesstimate if this is enough to win?
MG with circle
Pretty neat right? MG of clicking the Like button.
Please take a second. Full screen with clone. Clone analyzing pips.
Back to MG
Let’s say you place well, you have a ton of resources coming in, you are holding like 14 cards in your hand because you are just that loaded and a 7 is rolled. Congratulations you placed really well and got all those cards for nothing. There are only so many resources you will get throughout a game with 72 dice rolls, so losing that many resources on a 7 roll is a game losing scenario. If you don’t want to be the biggest loser, get it cause you lost a lot of cards, you can’t just settle for numbers, you have to also consider resource synergy so you can spend those resources. Your wood and brick numbers should be on par, as well as your wheat and ore numbers. Remember this, every dice roll, there is a 16.6% chance of a 7 being rolled and you losing half the cards in your hand. Assuming you have more than 7 cards. 16.6% is not only a really high number, but 7 is the highest probability outcome of any dice roll, and it’s basically guaranteed to happen at least once every 6 turns. So you better be able to spend at least every other turn. And if you are holding that many cards, there’s a good chance you are doing well enough in the game that you are going to be blocked pretty often, in which case you better have some knights handy.
Clone & I, clone is super happy with all his cards.
7 is rolled.
Clone Cries as he gives half to the bank.
Biggest loser comment, gets offended
I Block clone’s hex with a knight, offended.
MG
Clone offering cards to steal while I am about to steal one.
Which shouldn’t be too difficult because you have a 56% chance of drawing a knight card from the development card deck. There are 25 cards in the development card deck and it is broken down like this; 14 knights (56%), 5 victory points (20%), 2 road building’s (8%), 2 year of plenty’s and 2 monopoly’s.
MG with circle
Although you will be mostly getting knights. It’s still well worth the resources because if your 8 is blocked all game, those 10 resources you were expecting isn’t coming your way. 3 resources to defend 10 resources and slow down your opponents resource generation is well worth it.
MG with circle
If you are super eager to start up a game of Catan and use this information, you should first check out this video where a Catan champion shares his secrets about initial placements so that you have a 100% chance of being prepared for your next game.
Clone rolling dice. End card comes up. Clone gives to peak from behind..
Script v6
Catan and Poker are basically the same game. Except Poker players use one pretty simple tactic that makes them much better than Catan players. It’s so frequently used that it has even helped Poker grow into a huge spectator sport, which Catan is not, but deserves to be. You see these numbers? These represent the odds of any individual player winning with their hand. It’s such a standard for broadcasting the game that you don’t
Why is Poker more popular than Catan? As a Catan player, it’s easy to
I’m going to tell you exactly why Poker is a better game than Catan, this information is going to make you a better Catan player, and I’m going to do it all before I roll a 12. Roll dice. Now if you think & play like a Poker player, you would know that there is only a 2.38% chance of me rolling a 12 with these two dice. Those are really low odds and every good poker player would fold if they had a hand with those odds, unless they could bluff like a demigod (loki).
But how would a poker player know that percentage? Well the really good poker players have those percentages memorised or know how to calculate them, but for the rest of us normal people who can’t do that kind of math, the poker scene made the really smart move of showing us card percentages on screen during the game. This factor alone makes Poker a way better spectator sport than Catan. The thrill for viewers is knowing exactly who has the best chances, but then the still random element of the game brings surprise and delight. As a viewer you need a clear baseline expectation of what’s going to happen, otherwise it’s not really a surprise, it’s mostly just confusion.
If Catan tournaments were smart enough to implement this, their viewership would skyrocket. And it would look something like this. You’d have each player listed with their current hitpoints, did I say hitpoints, I mean victory points, and their development cards and how many of each resource they are holding. And below each resource is the % chance of them getting that resource with each dice roll. These numbers would be updated live each time they placed a new settlement or if the robber moved. It would be super interesting to viewers and incredibly useful for commentators to see these numbers clearly laid out.
But what about the Catan players? They don’t get to see these numbers and have to do the actual math for themselves, in their head. But I really doubt many players even bother to calculate the odds, they are happy to just assume that 12 will roll enough times to justify it as their wheat income. Let’s check out how that 12 roll is going. Yikes. Keep going buddy! I believe in you! Now, I bet you, that the higher up you go in the Catan rankings, the more the players are calculating the odds and factoring that into their decisions. But gosh darn it, that’s too much thinking for me. So I discovered a little shortcut.
You see these pips? These represent how many ways, out of the 36 possible combinations, the number 4 can come up with rolling two 6-sided die, which as you can see, is only 3 ways. There is only a 8.33% chance of this number being rolled. You can see the percentages of each dice total here. But there is no point in memorising these numbers because they don’t translate into practical value in the game. But this little shortcut will change that.
It turns out that the average game of Catan takes about 72 turns, that is 72 dice rolls. Which is an incredibly convenient number to do the simple and useful math we want to do. If we assume that a 4 is rolled 3 times every 36 rolls, then if we double that number, we can also assume that a 4 will be rolled 6 times every 72 rolls. So in an average game of Catan, you can expect 4 to be rolled 6 times. Pretty neat right? Let’s take a look at the game board of a Catan Nationship Championship Tournament Finals. And let’s see, based on the players initial settlements, how many of each resource they were expecting throughout the game. And if you watched my video on how a Champion picks their placements, you would see the genius in his strategy with these numbers on these resources, which means this is the perfect time to talk about resource synergy.
If you mismatch the resources you place on, especially with your initial settlements, you are going to find yourself severely unbalanced when it comes to spending your resources. You always want to try and get your brick and wood on a similar production number, and your ore and wheat on similar numbers too. This way, when they roll at an equal frequency, you can actually spend them and do things in the game instead of risking the 16.6% chance of a 7 being rolled every turn and you losing half the cards in your hand, assuming you have more than 7 cards. Another way to think about it is that you should play with the expectation of a 7 being rolled once every 6 turns. Now if you have good resource synergy, you should be able to spend almost every other turn, which will keep you out of the danger zone.
Speaking of danger zone (Archer), if you find yourself with a robber on your highest production hex, then that quick math you did at the start of the game is pretty much useless. This is where investing in development cards comes in handy and since you have a 56% chance of drawing a knight, those are really good odds that you can save your resource production. 3 resources for a development card to save 10 resources of income is totally worth it. And as a bonus, you’ll be slowing down your opponents income too.
MG side note of how many of each dev card in the dev deck with %’s.
But even with this handy trick, you might still be unsure of how to plan out your initial placements, which is why you should watch this video where that Catan National Champion from earlier, explains how he decides where to place. And if you don’t watch that video, you’ll still be waiting for that 12 wheat to be rolled.