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Subject: Change luck for strategy: use 3 dice!! rss

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Wichard Hulsbergen
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One of the worst things that can happen in Catan is that your numbers are NEVER rolled, and those of the one in the lead always.

I've thought up a nice idea how to change this:

- Throw three dice, with one of another colour (say red).
- You can now add up two of three numbers any way you like.
- Since "7" should always be a surprise, you can't choose 7. When the two non-red dice add up to 7, the robber occurs and you can't choose.

In Cities and Knights, use the red die for trade goods.

When using these rules, you have more influence on the income of yourself and others, so it will not happen that one person is left behind and you can effectively block a leader by not choosing his numbers. This blocking is not 100% ofcourse, since you only have a bit more choice.

Example 1:
red: 2
Other two: 3, 5.

You can now choose 2+3=5 or 3+5=8. (2+5=7 is prohibited (7).)

Example 2:
red: 1
Other two: 2, 5.

2+5 = 7 --> robber (no choice)

I think this rule is great for people that want a bit more strategy in the game without changing it's dynamics and basic principle.

Please let me know how you feel about it and if it works for you.
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Aaron Tubb
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This sounds cool. I like how you have more choice in what is rolled, but the chance of rolling the robber is the same as before. This looks like it may increase game time a bit, though.
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Aaron Zupancic

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I really like this idea and will give it a shot this weekend with our gaming group.

I think that you're right that when the two white dice equal 7 you should not be able to override it - you're stuck with the 7. However, I feel that if a red die and white die sum to 7 you should be able to choose it as one of your three possible results.

Perhaps it's part of your strategy to 1) get the robber off of your land, 2) put the robber on someone else, 3) get a resource card from someone because neither of the other two results yield resources for you at all or resources that you want.
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Isley
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I think being able to choose seven with the red dice would change the game too much by making it very good odds that a seven could be rolled each turn (too lazy to figure out the exact odds). Having to choose seven and not using the red dice for seven keeps the odds the same as the original of being forced to lose half your cards.
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Tim Seitz
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This seems like a great solution.

It would change the strategy a bit, from holding high probability numbers to horning in on some shared territory, especially if you are leading.

Settlers has been around awhile, hasn't anyone thought of this idea before?
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Bret Smith
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I think you have to allow the roller to choose 7 if they can using the red die, or the robber becomes _much_ less likely to be rolled. If I am correct then your proposed way has these odds:

2-3.10%
3-6.20%
4-9.30%
5-12.40%
6-15.50%
7-6.98%
8-15.50%
9-12.40%
10-9.30%
11-6.20%
12-3.10%

But if you let the roller choose a seven then:

2-2.78%
3-5.56%
4-8.33%
5-11.11%
6-13.89%
7-16.67%
8-13.89%
9-11.11%
10-8.33%
11-5.56%
12-2.78%

Which are the exact same odds as a "natural" roll of 2 dice. So, if you let the roller choose, while you have not changed any of the odds of a particular outcome appearing, you have allowed more of a choice on each individual roll, which I think was your intent.

Of course I might have completely flubbed the math or your intentions. If so, apologies ahead of time...



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kalle wong
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sounds really interresting
I will try with our playgroup.
but if the last calculation is right I think that might be a good thing to change to choose to have seven as well but take the thing that you may not choose not to take seven.
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Paul King
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BloodyJack wrote:
I think you have to allow the roller to choose 7 if they can using the red die, or the robber becomes _much_ less likely to be rolled. If I am correct then your proposed way has these odds:


I think you've missed the bit that says that a roll of 7 on the 2 non-red dice must be taken. That means that the chance of rolling a 7 is still 1 in 6.

I also don't think that your probabilities are correct - if you are calculating the probability of a player being able to select a particular number the probability of getting a 7 must be higher than the "natural" probability.
If you are using any other basis it needs to take into account the play situation - when will a '7' be better than the other options available ?

My quick estimate is that if a player WANTS a 7 he can get it with probability 15/36 instead of 6/36.
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Chris Farrell
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This sort of "solution" causes a lot of problems, and totally changes the game.

For example: in the basic game, loading up on individual numbers is usually a high-risk strategy. If your settlements have a limited spread of production numbers, your will tend to have feast or famine on resources, which is usually bad.

However, with this variant, when the players have a choice about how the numbers fall, the dynamics have totally changed. All of a sudden loading up is a good thing! Because on your turn, since you can effectively manipulate the dice, it's much more likely that you can choose to have your own settlements produce without giving anything to your opponents. And on the flip side, other players will tend to favor their own production if given the chance, and so are less likely to give you production if they have a choice.

Now, no longer is the placement of a settlement on a vertex a relatively comprehensible choice about probabilities. Everything has become much more complex. Now you have to figure out who else has those numbers, what other numbers they might have, and whether they are likely to choose them. All of a sudden a simple, easily-comprehensible game has become inordinately complicated.

This may work as long as people don't adjust their style of play to accommodate the change. But pretty soon, people will learn that to win they have to game the choices involved in the third dice, and things will get out of hand.
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Richard Young
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cfarrell wrote:
Now, no longer is the placement of a settlement on a vertex a relatively comprehensible choice about probabilities. Everything has become much more complex. Now you have to figure out who else has those numbers, what other numbers they might have, and whether they are likely to choose them. All of a sudden a simple, easily-comprehensible game has become inordinately complicated.


In addition to the removal of the "get hosed early and you're hosed for good" thing, I think you've given us a number of excellent additional reasons to embrace this idea. I might actually consider playing this game again with this variation in play. I like that there should be more things to think about than what the stupid dice are going to do this time (or again)...
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Bret Smith
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Paul, you are right of course, let's try this again:

I believe here are the Max %s you can expect to roll each outcome if you _WANT_ the listed outcome:

2-6.48%
3-12.04%
4-18.52%
5-24.07%
6-30.56%
7-16.67%
8-30.56%
9-24.07%
10-18.52%
11-12.04%
12-6.48%

This system IS weighted towards even #s. As you can never be forced to choose any Odd # (other than 7) but you CAN be forced to choose 2, 4, 6, 8, 10, and 12. 2 occurs when the red die is a 6, and the two normal are 1-1. The 4 when the red die is a 5 and the two normal are 2-2 etc....



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Wichard Hulsbergen
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Thanks for all the replies!

@ Chris "All of a sudden a simple, easily-comprehensible game has become inordinately complicated. (..) and things will get out of hand"

If you don't want to add strategy to Catan and like it like it is, then please do not try this variant. I do not want to be held responsible for thing to get out of hand

@ Bret your numbers are right. I've done some math myself.
Traditionally, these are the odds for numbers:
2 - 2,8%
3 - 5,6%
4 - 8,3%
5 - 11,1%
6 - 13,9%
7 - 16,7%
8 - 13,9%
9 - 11,1%
10 - 8,3%
11 - 5,6%
12 - 2,8%

As you can see, the odds to throw a number you want has been multiplied by 2.2 for each number. This means that while the chance to throw 7 has not changed (still 1 out of 6), all the other odds are much better.
A thing that does not turn up in these numbers, is that some like "2") never turns up when the numbers give you three choices, while others (like "6") are more easily avoided. This math is beyond me, but frankly I don't care.

Let's just play and see how it goes!
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Gavin Wynford-Jones
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Hey, why not just chuck away the dice and merely pick the number you want instead!

There are many flaws in your suggestion, but the three key ones are:

- you unbalance the relationship between the hex numbers, the odds of rolling those numbers, and their relative locations on the board;

- even numbers, even with the choice option, will tend to come up more than odd numbers

- players will favour their own hex numbers, so trading will diminish rapidly.

Bad variant!

Gavin
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Aaron Tubb
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This variant might be especially good when combined with the two player variant (each player gets 3 settlements). I imagine it would speed up the game considerably, without changing the feel of the game.
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L. Scott Johnson
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Excellent variant. Especially nice and clean improvement to the luck factor without introducing any significant flaws (or at least, the good from the variant outweighs the bad).
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Maarten D. de Jong
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gavingva wrote:
even numbers, even with the choice option, will tend to come up more than odd numbers

Forgive me for being thick here, but how do you arrive at this conclusion?
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Andy K.
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A very interesting and simple variant. Thumbs up!

Please report back about how this works out. Does it make it too easy to get resources and shut other players out? My first thought is that this variant will increase trading because all players can more easily gain resources, but of course only in those resources they occupy.

One idea that instantly comes to mind is to pay a penalty for the privilege of using the red die. Perhaps discard one resource to use the red die. This would devolve however to a quick calculation of "can I get more than I lose ". Another approach would be to discard one resource at random from your hand; maybe the player to the left of the active player could choose from the active player's hand?
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Gavin Wynford-Jones
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cymric wrote:
gavingva wrote:
even numbers, even with the choice option, will tend to come up more than odd numbers

Forgive me for being thick here, but how do you arrive at this conclusion?


With three dice, there are basically six possible results. Each die will show either an odd or an even face. The possible combinations are:

Die 1 - Die 2 - Red die
Odd - odd - odd (cannot roll 7)
Odd - odd - even (cannot roll 7)
Odd - even - even (1 in 6 chance of a 7)
Odd - even - odd (1 in 6 chance of a 7)
Even - even - odd (cannot roll 7)
Even - even - even (cannot roll 7)

In the first and last cases, the combined result forces to an even result. Only in the middle cases can you select for odd or even. In only two of those cases can the 7 occur. Thus, 1 in 3 of the die rolls give an even result regardless of the choice.

In cases three and four, on the base dice, you have a 1/6 chance of rolling a 7, and a 5/6 of being able to choose. Out of those remaining results, 18 give an even number and 12 give an odd number. (The imbalance is caused by extracting the 7, which is an odd number.) Now you factor in the red die. In half the cases it will be even and half it will be odd. That means that 9 even numbers will be forced to stay even and 6 odd numbers will be forced to become even. That leaves only 15 of the original 36 rolls that can be chosen as odd. In order for evens not to preponderate in these cases, all 15 results would have to be consistently chosen to force an odd number.

Out of the remaining rolls, some will also be chosen as being even. Thus, even results will preponderate.

Gavin
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Greg Jones
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cfarrell wrote:
This sort of "solution" causes a lot of problems, and totally changes the game.

For example: in the basic game, loading up on individual numbers is usually a high-risk strategy. If your settlements have a limited spread of production numbers, your will tend to have feast or famine on resources, which is usually bad.

However, with this variant, when the players have a choice about how the numbers fall, the dynamics have totally changed. All of a sudden loading up is a good thing! Because on your turn, since you can effectively manipulate the dice, it's much more likely that you can choose to have your own settlements produce without giving anything to your opponents. And on the flip side, other players will tend to favor their own production if given the chance, and so are less likely to give you production if they have a choice.


I don't know. If you load up on a single number, then start to take the lead, all of a sudden all the rest of the players are never picking your number. You can only get paid out on your own roll. But if you diversify, then it will be hard for them to avoid giving you resources. It might work out about even. Either collect moderate resources on every turn, or lots on your own turn.

One idea to offset this though. You don't get to pick the dice value on your own turn. You get to pick the dice value on the player to your left's turn. That way, if you use the strategy on loading up on a single number, you will collect your big load of resources, and then risk the robber for several turns before you can build.
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Jeff Luck
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I think you missed two - there are actually 8 combinations:

Die 1 - Die 2 - Red die
Odd - odd - odd (cannot roll 7)
Odd - odd - even (cannot roll 7)
Odd - even - even (1 in 6 chance of a 7)
Odd - even - odd (1 in 6 chance of a 7)
Even - odd - odd (1 in 6 chance of a 7)
Even - odd - even (1 in 6 chance of a 7)

Even - even - odd (cannot roll 7)
Even - even - even (cannot roll 7)

One set gets counted twice, which wouldn't matter except in this kind of discussion.

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Richard Young
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gavingva wrote:
Hey, why not just chuck away the dice and merely pick the number you want instead!


Well, no-one is really suggesting that are they? As it is, what you have is an elaborate game of Yahtzee (as another poster nicely summarized: "theme-attached Yahtzee"). This interesting idea for a variant still produces variable results but ones you have just a little more control over.
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Quote:
Die 1 - Die 2 - Red die
Odd - odd - odd (cannot roll 7)
Odd - odd - even (cannot roll 7)
Odd - even - even (1 in 6 chance of a 7)
Odd - even - odd (1 in 6 chance of a 7)
Even - even - odd (cannot roll 7)
Even - even - even (cannot roll 7)


First, if die 1 must be odd and die 2 must be even, there is a 1 in 3 chance of rolling a 7.

Second, this seems like a deceptive way to list the possibilities. You have left out the following combinations.

Even - odd - even (1 in 3 chance of a 7)
Even - odd - odd (1 in 3 chance of a 7)

By dividing the dice up into groups delimited by even and odd, all possible combinations must be presented.

Also, in the original cases, there are more choices for odd numbers than there would appear.
Odd-odd-odd : all even.
Odd-odd-even : 1 even - 1 odd (2/3) or 1 even - 2 odd choices (2/9) or one even (1/9)
Odd-even-even : 7 (1/3) or 2 odd - 1 even (2/9) or 1 odd - 1 even (4/9)
Odd-even-even : 7 (1/3) or 2 odd - 1 even (2/9) or 1 odd - 1 even (4/9)
Even-odd-odd : 7 (1/3) or 2 odd - 1 even (2/9) or 1 odd - 1 even (4/9)
Even-odd-even : 7 (1/3) or 2 odd - 1 even (2/9) or 1 odd - 1 even (4/9)
Even-even-odd : 1 even - 1 odd (2/3) or 1 even - 2 odd choices (2/9) or one even (1/9)
Even-even-even : all even

Overall, even will be forced 5/18 times and odd will be forced 1/6 times. Of the remaining, there will be a choice between 1 odd and 1 even 7/18 times and between two odds and one even 1/6. If these are chosen at the rates indicated in the ratios, evens will be chosen/rolled 19/36 as compared to 18/36 on 2d6, giving a slight advantage to the evens.


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Gavin Wynford-Jones
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Bubslug wrote:
gavingva wrote:
Hey, why not just chuck away the dice and merely pick the number you want instead!


Well, no-one is really suggesting that are they? As it is, what you have is an elaborate game of Yahtzee (as another poster nicely summarized: "theme-attached Yahtzee"). This interesting idea for a variant still produces variable results but ones you have just a little more control over.


The game as designed includes a balancing mechanism so that no one intersection is vastly better than any other (within limits). Variants such as this one, and one where you randomly assign the number chits, affect the balance without applying a counterbalance.

Hence you might as well go one step further and just pick the numbers you want. It makes as much sense and gives you even more control. (What's the icon for being facetious?)

Gavin
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Bret Smith
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Might I suggest a slight variation to your variation? ?

Roll two red dice and two white dice.
If the white dice = 7 then Robber (no choice).
If the red Dice = 7, then use the sum of the white dice (no choice).
Otherwise choose between using the sum of the red dice or the sum of the white dice.

I believe this variation no longer favors the even numbers, still keeps the frequency of the Robber the same, and yet allows for more control of your outcome.

Thoughts?
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David Liu
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After excluding '7', the probability of getting an even number on 2d6 is higher. Heck, there is more even numbers to start with(6:4 without 7). So I don't think forcing even numbers a few more times should be a problem.

2 1/36
3 2/36
4 3/36
5 4/36
6 5/36
7 6/36
8 5/36
9 4/36
10 3/36
11 2/36
12 1/36

even: 18/36 odd: 12/36 (without 7)

Anyway, I think this variant is pretty interesting, my group always wanted more strategy/decisions in Settlers. I'm think they would like to have the option to make a 7 when possible instead of forcing the other numbers. (but that simply turns into choose any 2 dice from 3d6)

I'll try this when we get the chance...
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