Change Refund Amounts for Flat Rate games

[dancingchiapet]

Change Refund Amounts for Flat Rate games

I came across this when playing risk with some friends.

In regards to a flat rate games where the pay out is 4,6,8, or 10, 10 obviously should be given to the rarest card combination. Currently, 10 armies is paid out for one color of each, but it is in fact the most likely card combination. Here is the math:

For the Classic map there are 42 territories/cards made up by 14 reds, 14 greens, and 14 blues.

Let us look at a hypothetical situation in which only one player is recieving cards and always draws the most likely color.

Player one recieves a red card. This means in the deck there are 13 reds, 14 greens, and 14 blues. This means that player one will most likely next draw a green or a blue (because there are more in the deck). Going along with that we'll say player one next draws a green card. This means the deck now is made up of 13 reds, 13 greens, and 14 blues. Blue is the most likely card to get next, which will give player one 10 armies.

There are a bunch of different senarios depending on the different number of players, but it is never harder to get one color of each, statistically speaking.




Going just by math alone it would probably make the most sense to have a set of the same color be worth the same as any other color, since they all have the same probabilitiy. So possibly 10 armies for 3 cards of the same color and 6 armies for a set of one of each color.

A very easy change though would simply be: 4 for 1 of each, 6 for 3 red, 8 for 3 green, 10 for 3 blue.





The priority is only about a 2, but it is still something that needs to be looked at at some point.

[joeyjordison]

nope. ur lookin at it wrong dude. imagine every card is the same. every card has the same probability. the only reason 1 card becomes more likely to appear is because some1 else picked 1 of the others. but its rare that someone gets 2 cards in a row in which case the chances r always the same. at very close mathematical investigation u will find that the chances of getting 3 of the same or 1 of each will differ depending on the number of players in the game and wether they get a card. besides the difference is so small even at maximum odds its would b about 1%more likely to occur... they r fine as they r. its how risk is played.

new people would get really confused by it if they hav played board risk

[dancingchiapet]

if you draw a red card, the deck has 13 reds, 14 greens, and 14 blues.

There are 13 out of 41 cards you could draw of the same color and 28 out of those 41 cards that would be different. So, getting a set of the same color is more unlikely. It's basically 33% for the same color versus 66% for a different color.

[Lone.prophet]

than the third card u need for 3 different is 33% so it evens out

[dancingchiapet]

i know the odds change depending on the number off players and which cards are drawn, but i already made a note of that.

In regards to the difference made by other cards being drawn, the senario I created was what is most mathematically probable, which is how the rules should be decided, by what is most likely to happen in a game.

In regards to the effect of mulitple players, I could type out a more detailed view of that effect, but I'll have to do it later today. I have looked it to it and I already pointed out that it would change the odds, but it would never make it so that getting one color of each is harder than getting all the same color. The closest situation to that is when game are played with a number of players that is a multiple of 3, so realistically 6 since online we dont play with 3 or 9. With 6 players, all the different combinations are statistically the same.

[dancingchiapet]

than the third card u need for 3 different is 33% so it evens out

alright, so lets draw this out using the most likely possibility.

draw red card.
13 red, 14 green, 14 blue
draw green card.
13 red, 13 green, 14 blue.

the most likely card is blue because the are the most left in the deck, plain and simple. if i need to draw this out further, ill do it later today.

[Lone.prophet]

though u dont no it is more likely 2 get a red or green than a blue

[IT3USN]

Change Refund Amounts for Flat Rate games

I came across this when playing risk with some friends.

In regards to a flat rate games where the pay out is 4,6,8, or 10, 10 obviously should be given to the rarest card combination. Currently, 10 armies is paid out for one color of each, but it is in fact the most likely card combination. Here is the math:

For the Classic map there are 42 territories/cards made up by 14 reds, 14 greens, and 14 blues.

Let us look at a hypothetical situation in which only one player is recieving cards and always draws the most likely color.

Player one recieves a red card. This means in the deck there are 13 reds, 14 greens, and 14 blues. This means that player one will most likely next draw a green or a blue (because there are more in the deck). Going along with that we'll say player one next draws a green card. This means the deck now is made up of 13 reds, 13 greens, and 14 blues. Blue is the most likely card to get next, which will give player one 10 armies.

There are a bunch of different senarios depending on the different number of players, but it is never harder to get one color of each, statistically speaking.




Going just by math alone it would probably make the most sense to have a set of the same color be worth the same as any other color, since they all have the same probabilitiy. So possibly 10 armies for 3 cards of the same color and 6 armies for a set of one of each color.

A very easy change though would simply be: 4 for 1 of each, 6 for 3 red, 8 for 3 green, 10 for 3 blue.





The priority is only about a 2, but it is still something that needs to be looked at at some point.

you're thinking here as wrong and rather than sit here and try to explain the logic.....think about this. This is a really old board game which the rules were thought about years ago. don't go changing the BASIC rules of the game. I realize as this site grows larger and larger, we keep improvising new rules, maps, and play. However, they are all based on BASIC rules. Now, if you want to contact hasbro and debate them on probabilities, be my guest. If anything, you can look at having more realistic cards. I believe the real game has calvary, canons and infantry.

[boberz]

mathmatically dancingchia pet is correct. However i believe that in the interests of the game (for reasons stated by other people) it should not be changed. I think it was quite sad to spend quite as much time as it seems you have on this. Perhaps if you want to limit amount of luck created by cards, play no card games. However in future i agree this could be an option in creating a game (along with flat rate, escalating and no cards) but at such a low priority it would never be worth doing, sorry.

[dcowboys055]

than the third card u need for 3 different is 33% so it evens out

alright, so lets draw this out using the most likely possibility.

draw red card.
13 red, 14 green, 14 blue
draw green card.
13 red, 13 green, 14 blue.

the most likely card is blue because the are the most left in the deck, plain and simple. if i need to draw this out further, ill do it later today.

so what if i draw a red
13-red 14-green 14-blue
then xxx goes and draws a green
13-red 13-green 14-blue
then xxx goes and draws a blue
13-red 13-green 13-blue
then xxx goes and gets a blue
13-red 13-green 12-blue
then xxx goes and gets a green
13-red 12-green 12-blue

now its my turn and now the chances are i will get a 2nd red...

you logic only works if you're the only one getting cards

[spiesr]

Since conquer club doesn't use a "real deck" the colors of cards are assinged when you get them so you always have 1/3 chane of getting any color.

[IT3USN]

Since conquer club doesn't use a "real deck" the colors of cards are assinged when you get them so you always have 1/3 chane of getting any color.

an excellent point

[qeee1]

Since conquer club doesn't use a "real deck" the colors of cards are assinged when you get them so you always have 1/3 chane of getting any color.

I thought it used a deck triple the standard size, with one red, green and blue for each territory?

[sully800]

No, once a card is chosen it is out of the deck until it is played. I remember lack saying that before (so you could never draw two of the same card at once). I also believe the colors are randomly assigned, which shoots this whole suggestion to hell, but I'm not sure.

[everywhere116]

Since conquer club doesn't use a "real deck" the colors of cards are assinged when you get them so you always have 1/3 chane of getting any color.

As I was reading this thread I was thinking that same very point. I have seen games when someone got a card as one color and the next person to get the same got it in another color.

[lackattack]

No, once a card is chosen it is out of the deck until it is played. I remember lack saying that before (so you could never draw two of the same card at once). I also believe the colors are randomly assigned, which shoots this whole suggestion to hell, but I'm not sure.

Right on both points

[maniacmath17]

Gather around boys and girls, you are about to get a lesson.

If you are given 3 random cards that have made a set, the probability of the set being one of each color is twice as probable as it is of being 3 of the same color. Here's the reasoning.

Chances of picking any color on the first card 1/1

Chances of picking that same color for the 2nd card is 1/3 and chances of picking a color different than that color is 2/3

Chances of picking the same color for a 3rd turn is 1/3 and chances of picking the final color in a 3 different color set is 1/3

So that makes chances of a set with the same color: 1 x 1/3 x 1/3 = 1/9
And chances of a mixed set: 1 x 2/3 x 1/3 = 2/9

I actually like the way the flat rate cards are now, but I think it should be known that a mixed set is twice as likely as a same color set.

[Evil Semp]

Since conquer club doesn't use a "real deck" the colors of cards are assinged when you get them so you always have 1/3 chane of getting any color.

As I was reading this thread I was thinking that same very point. I have seen games when someone got a card as one color and the next person to get the same got it in another color.

This has happened to me. I trade a card, finish my turn and get the same card but I don't remember if the color was different.

[Fantius]

Very nice, maniacmath17. I would not have guessed that outcome.

I have empirically confirmed your results.

[dancingchiapet]

mathmatically dancingchia pet is correct. However i believe that in the interests of the game (for reasons stated by other people) it should not be changed. I think it was quite sad to spend quite as much time as it seems you have on this. Perhaps if you want to limit amount of luck created by cards, play no card games. However in future i agree this could be an option in creating a game (along with flat rate, escalating and no cards) but at such a low priority it would never be worth doing, sorry.

There is no reason to insult me for bringing this up. This is a suggestion board for any subject that might improve upon the game and thats all I am trying to do by bringing this up. I know it's a low priority and I clearly stated that in my original post. If it's so sad to read what I've typed, just don't worry about it.

[IT3USN]

There is no reason to insult me for bringing this up. This is a suggestion board for any subject that might improve upon the game and thats all I am trying to do by bringing this up. I know it's a low priority and I clearly stated that in my original post. If it's so sad to read what I've typed, just don't worry about it.

I don't believe anyone has insulted you in this thread. You opened a discussion and people gave you their input. That is what this forum is for. Most of the suggestions here get shot down so don't feel bad. I think the majority thought you were correct but didn't want to change the game play.

[IT3USN]

just out of curiosity, what are the cahnces of someone getting 10 strait red cards in a flat rate game? cause it is happening to me!!! well, 10 and counting.....we'll see how long this keeps up.

[boberz]

mathmatically dancingchia pet is correct. However i believe that in the interests of the game (for reasons stated by other people) it should not be changed. I think it was quite sad to spend quite as much time as it seems you have on this. Perhaps if you want to limit amount of luck created by cards, play no card games. However in future i agree this could be an option in creating a game (along with flat rate, escalating and no cards) but at such a low priority it would never be worth doing, sorry.

There is no reason to insult me for bringing this up. This is a suggestion board for any subject that might improve upon the game and thats all I am trying to do by bringing this up. I know it's a low priority and I clearly stated that in my original post. If it's so sad to read what I've typed, just don't worry about it.

sorry wasnt meaning to offend had had a bad day and had a short temper but the rest of my post stands, it should be another option not changing the flat rate cards themselves. Perhaps you could call the new system "flate rate version 2"

[dancingchiapet]

just out of curiosity, what are the cahnces of someone getting 10 strait red cards in a flat rate game? cause it is happening to me!!! well, 10 and counting.....we'll see how long this keeps up.

1/1 x 1/(3^(n-1)

so

1/(3^9) = 1/19683

0.005% Chance

[dancingchiapet]

actually thats for any one color

for red only multiply that by 1/3 again. so yeah, its pretty unlikely