Flat rate card strategy?

[Zaphod]

OK - Just wondering what other's would do?

Just defeated a player and acquired his 2 cards - upon ending my turn I have 5 cards.

3 are blue - I own one.
1 is red - which I own.
and 1 green.

Do you turn in the mixed set now and build up cards again or do you turn in 3 blue and hope for another blue when after your next turn?

[tahitiwahini]

OK - Just wondering what other's would do?

Just defeated a player and acquired his 2 cards - upon ending my turn I have 5 cards.

3 are blue - I own one.
1 is red - which I own.
and 1 green.

Do you turn in the mixed set now and build up cards again or do you turn in 3 blue and hope for another blue when after your next turn?

Quick answer, you turn in the mixed set as soon as possible.

[yeti_c]

Always turn in the mixed - you may not get another mixed next turn... thus you'll be down 2 armies...

The point is much more valid with Red cards obviously as blue's are the best 'straight' set.

C.

[tahitiwahini]

Longer answer:

Let's adopt this notation (RGB) --> n,

where R is the number of red cards, G the number of green, B the number of blue, and n the number of armies you can claim by turning in the set.

So, you start with (213). There are two cases:

Case 1:
(213) --> 10, leaving (102); based only on this you would prefer case 1 because you'd be getting 2 more armies.

For your fourth card you have a 33% chance each of receiving a R/G/B card:
(102) + R = (202) see below
(102) + G = (112) --> 10
(102) + B = (103) --> 8
So, on average with your next card you will have a set worth 18/3 = 6 armies. You would prefer case 1 again because you'd be getting 1.33 more armies.

For your fifth card you have a 33% chance each of receiving a R/G/B card:
(202) + R = (302) --> 4
(202) + G = (212) --> 10
(202) + B = (203) --> 8
So, on average with your next card you will have a set worth 22/3 = 7.33 armies. You would prefer case 1 again because you'd be getting 0.67 more armies.

Case 2:
(213) --> 8, leaving (210)

For your fourth card you have a 33% chance each of receiving a R/G/B card:
(210) + R = (310) --> 4
(210) + G = (220) see below
(210) + B = (211) --> 10
So, on average with your next card you will have a set worth 14/3 = 4.67 armies.

For your fifth card you have a 33% chance each of receiving a R/G/B card:
(220) + R = (320) --> 4
(220) + G = (230) --> 6
(220) + B = (221) --> 10
So, on average with your next card you will have a set worth 20/3 = 6.67 armies.

So at every step on the way you would prefer case 1 over case 2.

[Zaphod]

Wow - cool analysis. I like it when an answer is backed up with numerical proof.

Thanks.

[RobinJ]

I always love your "long answers" tahitiwahini

[Molacole]

OK - Just wondering what other's would do?

Just defeated a player and acquired his 2 cards - upon ending my turn I have 5 cards.

3 are blue - I own one.
1 is red - which I own.
and 1 green.

Do you turn in the mixed set now and build up cards again or do you turn in 3 blue and hope for another blue when after your next turn?

wow you'll get 14 armies if you turn in a mixed set and you're asking if you should turn in a blue set for 10? that's some funny shit...

[nagerous]

if you own all three blues then turn it in or if you own 2 blues and no of any colour then maybe

[oVo]

Simpler still: the mixed set (with 2 territories) is worth 14, while the blue set is worth 10.
How hard can it possibly be to choose which is best?

[tahitiwahini]

Simpler still: the mixed set (with 2 territories) is worth 14, while the blue set is worth 10.
How hard can it possibly be to choose which is best?

You're right about that, although I didn't factor that into my calculation. I missed the part where he said he owned the country on the card the first time I read his post. He gets 2 country card bonuses if he cashes in a mixed set versus only 1 if he cashes in the blue set. In this case it makes cashing the mixed set all the more profitable.

In the general case, it's always best to cash in the mixed set for a couple reasons. One, the mixed set is the most valuable set. Two, you really don't want your hand seeded with 2 of any color, because it make it less likely you will be able to form a mixed set in the future.

So even if in the original example he owned the countries on all three blue cards (and didn't own the countries on all the other cards) it would still be better to cash the mixed set because he would get the same number of armies, but in case 1 he would be able to freely deploy 10 armies, while in case 2 he would be able to freely deploy only 8 armies (the other armies being placed on the countries named on the cards cashed). Then with his next card he would on average get 1.33 more armies in case 1 than 2, and with his next card after that he would on average get 0.67 more armies in case 1 than 2. On top of that, if he did have to go all the way to the fifth card to get another set to cash, when he cashed that set he would be left on average with more valuable hands in case 1 [(002), (101), (200) - having 3 red cards and 3 blue in all the possible hands] than case 2 ([(020), (200), (110) - having 3 red cards and 3 green in all the possible hands].

So, no it's not hard to choose in this case.

[Zaphod]

OK - that was just this situation - I've had the same card set up in a German game, but w/o owning any of the territories. I guess that would of been a better example for figuring preference.

Owning 2 of a mixed set certainly makes the decision easier.

[detlef]

Wow - cool analysis. I like it when an answer is backed up with numerical proof.

Thanks.

How's this for numerical proof:
A mixed set is worth 10 and a blue set is worth 8. Turn in the mixed set.

[Zaphod]

Wow - cool analysis. I like it when an answer is backed up with numerical proof.

Thanks.

How's this for numerical proof:
A mixed set is worth 10 and a blue set is worth 8. Turn in the mixed set.

Yeah - but I like the more detailed answer calculating in the potential for having another set on my next turn.

[detlef]

Wow - cool analysis. I like it when an answer is backed up with numerical proof.

Thanks.

How's this for numerical proof:
A mixed set is worth 10 and a blue set is worth 8. Turn in the mixed set.

Yeah - but I like the more detailed answer calculating in the potential for having another set on my next turn.

I guess I just thought it was a stupid question. Either case, you've got a 1 in 3 chance of making the set that you didn't cash so what's the question? The fact that you actually held two of the countries in the mixed set and one of the blue makes it an even more stupid question.

I don't know, let me make this answer longer so you'll like it better. First thing I'd do, is count to 100 and then count backwards. When you get to 64 stop and think about how many that is. That number is one less than the number of teams invited to the NCAA BBall tourney. Then stop and think about the number 35. That number is half of 70. Are you following me?

OK, now when you get to 10, decide if that number is larger than 8. OK, now if you could either have $10 right now and have a 1 in 3 chance of having $8 more would you take that or take $8 now and have a 1 in 3 chance of having $10 more.

[terrafutan]

lol

[khazalid]

if say you have a red, a green and 3 blues owning none of the territories... isnt it better to trade the 3 blues because it makes it statistically more likely that then next card you will draw will be a blue? i dont think it applies to green or red sets because of the lower bonus etc. maybe tahiti expained this already but i wasnt following it too well : /

[tahitiwahini]

if say you have a red, a green and 3 blues owning none of the territories... isnt it better to trade the 3 blues because it makes it statistically more likely that then next card you will draw will be a blue? i dont think it applies to green or red sets because of the lower bonus etc. maybe tahiti expained this already but i wasnt following it too well : /

If you accept that the cards are selected randomly and independently then no, the fact that you trade the 3 blues does not make it statistically more likely the next card you draw will be a blue.

Let's imagine a six-sided die that's perfectly balanced so it can not be expected to land on any one side any more often than any other side. You want to know what the likelihood that you will roll a six with the die. There are six possibilities, so you have a one-in-six chance of rolling a six, or put another way, 17% of the time you can expect to roll a six.

You roll the die and it turns up six. Now you want to know what the likelihood that you will roll a six with the die. There are six possibilities, so you have a one-in-six chance of rolling a six, or put another way, 17% of the time you can expect to roll a six.

So you roll the die again and it turns up six. Now you want to know what the likelihood that you will roll a six with the die. There are six possibilities, so you have a one-in-six chance of rolling a six, or put another way, 17% of the time you can expect to roll a six.

So you roll the dice again and it turns up six. Now you want to know....

I think you get the point. The die has no short-term memory, the die has no long-term memory, the die has no memory at all. The die has no understanding of what it did in the past. The die doesn't understand that it should stop rolling a six. The die isn't interested in making itself appear more random. The die doesn't even understand that it is being observed. To put it succinctly the die just doesn't give a damn.

This is the real reason that there's no such thing as a streak outside of an observer's head. A streak is an interpretation put onto the past throws of the die by a person observing the die. To put it another way: 6 6 6 6 6 6 6 6 6 6 6 6 6 6, is no more a streak, than 1 4 5 2 3 5 2 6 3 4 1 3 2 5. They are equally likely to happen.

Hope this helps.

[detlef]

if say you have a red, a green and 3 blues owning none of the territories... isnt it better to trade the 3 blues because it makes it statistically more likely that then next card you will draw will be a blue? i dont think it applies to green or red sets because of the lower bonus etc. maybe tahiti expained this already but i wasnt following it too well : /

If you accept that the cards are selected randomly and independently then no, the fact that you trade the 3 blues does not make it statistically more likely the next card you draw will be a blue.

Let's imagine a six-sided die that's perfectly balanced so it can not be expected to land on any one side any more often than any other side. You want to know what the likelihood that you will roll a six with the die. There are six possibilities, so you have a one-in-six chance of rolling a six, or put another way, 17% of the time you can expect to roll a six.

You roll the die and it turns up six. Now you want to know what the likelihood that you will roll a six with the die. There are six possibilities, so you have a one-in-six chance of rolling a six, or put another way, 17% of the time you can expect to roll a six.

So you roll the die again and it turns up six. Now you want to know what the likelihood that you will roll a six with the die. There are six possibilities, so you have a one-in-six chance of rolling a six, or put another way, 17% of the time you can expect to roll a six.

So you roll the dice again and it turns up six. Now you want to know....

I think you get the point. The die has no short-term memory, the die has no long-term memory, the die has no memory at all. The die has no understanding of what it did in the past. The die doesn't understand that it should stop rolling a six. The die isn't interested in making itself appear more random. The die doesn't even understand that it is being observed. To put it succinctly the die just doesn't give a damn.

This is the real reason that there's no such thing as a streak outside of an observer's head. A streak is an interpretation put onto the past throws of the die by a person observing the die. To put it another way: 6 6 6 6 6 6 6 6 6 6 6 6 6 6, is no more a streak, than 1 4 5 2 3 5 2 6 3 4 1 3 2 5. They are equally likely to happen.

Hope this helps.

Your patience knows no boundries. Tahitiwahini, the Mother Theresa of Conquer Club.

[andreweberman]

When you have a rainbow set, do you always play it right away or do you hold on to it for various reasons and play it later (assumes flat rate game)?

[iAnonymous]

If I need extra troops for something, I play them. Sometimes, I hold them until I can eliminate someone and take the opponent's cards, so I can play multiple sets at once.

[mathgeni]

if i have a rainbow set i play it right away so that i can take more territories and hopefully get the extra armies to start my next turn due to having more territories

[detlef]

I almost always hold it for at least a turn. Provided I'm not so weakened that I could face elimination, I like to be the last one to play a set. Typically, the first guy to do so gets hit back by at least one of the next ones to cash in. If you can fly under the radar, you can cash your set in, seize whatever advantage you wanted to seize, and not be as likely to be attacked by someone with a set to cash in.

Learning to hold off on cashing in early sets was perhaps the most important things I learned about being a better player.

In team games, well at least 2 v 2 or 3 v 3 (or I suppose the latest stupid game style to be created 1 v 1), this matters less because there's no way to fly under the radar. Thus, because these games are disproportionally about luck, you seize the good fortune you have by making a mixed set with 3 cards and cripple the other team early.

[RobinJ]

I would usually cash in straight away - I see no point in risking bonuses, etc by holding on to them. Then again, it could make me appear to strong and there is always the possibility of gaining some of the card territories for extra armies first. So, I guess it depends on the situation (you should have it in your poll)

[KennyC]

I am assuming you are playing flat rate since rainbow had to be specified (I could see holding on to them for as long as possible at the start of an esclating game). I never saw any use in holding them for a turn until I read this(detlef makes a strong point about holding at the start), so good question I'm glad I learned something.

[jako]

I almost always hold it for at least a turn. Provided I'm not so weakened that I could face elimination, I like to be the last one to play a set. Typically, the first guy to do so gets hit back by at least one of the next ones to cash in. If you can fly under the radar, you can cash your set in, seize whatever advantage you wanted to seize, and not be as likely to be attacked by someone with a set to cash in.

Learning to hold off on cashing in early sets was perhaps the most important things I learned about being a better player.

wow i always cash them in so i can get the big boost in troops and comeback to do a territory sweep and get more troops nex turn for having more territories but now that detlef mentioned being hit by the person to cash in their set after me, i will try to hold on to them untl someone else cashs before me unless im near elimintation.