The probability of drawing a hand of all research cards in a 7 Wonders round with 3 players is lower than drawing a similar hand in a round with 6 players, assuming the proportion of research cards stays the same in both cases.
For 1/3 research cards in the deck, the probabilities are (exact on the left, computer simulation result on the right):
3 Players: 8.5999e-006 8e-006
6 Players: 0.00012721 0.000143
Matlab code:
decks = [7,14
14,28]; % number of cards of each type
deckCards = [1,4,7,10,13,16,19
1,7,13,19,25,31,37]; % cards received by Player 1
rDecks = [0,0];
nReps = 1000000;
for reps = 1:nReps
for nDeck = 1:2
deck = [zeros(1,decks(nDeck,1)),ones(1,decks(nDeck,2))]; % make the deck
deck = deck(randperm(length(deck))); % shuffle
if(all(deck(deckCards(nDeck,:))==0)) % are all the same?
rDecks(nDeck) = rDecks(nDeck) + 1;
end
end
end
rDecks = rDecks / nReps;
disp([prod(1:7)/prod(15:21), rDecks(1)]);
disp([prod(8:14)/prod(36:42), rDecks(2)]);

Can you create the probability curves for less than 7 cards as well? if the probability can be placed in a curve it could be that we were both right, depending on what shape the two curves are at :P

Sure -- with fewer players, it is more likely to get a proportion of research cards in your hand that is close to the proportion of research cards in the deck. Blue is 3 players, Green is 6 players:
1/3 of the cards are research cards:

Okay, cool to know. Seems you were right: higher number of players make it slightly more likely that you get more 'clumping' of cards. I was gonna say that the lower numbers for 0 to 2 cards show the opposite but considering the scenario, if you don't get the cards, someone else will, which is what we were discussing in the first place. Thanks for running the maths.

Probabilities in Seven WondersGabi TeodoruPosted 7/23/12 1:30 PMThe probability of drawing a hand of all research cards in a 7 Wonders round with 3 players is lower than drawing a similar hand in a round with 6 players, assuming the proportion of research cards stays the same in both cases. For 1/3 research cards in the deck, the probabilities are (exact on the left, computer simulation result on the right): 3 Players: 8.5999e-006 8e-006 6 Players: 0.00012721 0.000143 Matlab code: decks = [7,14 14,28]; % number of cards of each type deckCards = [1,4,7,10,13,16,19 1,7,13,19,25,31,37]; % cards received by Player 1 rDecks = [0,0]; nReps = 1000000; for reps = 1:nReps for nDeck = 1:2 deck = [zeros(1,decks(nDeck,1)),ones(1,decks(nDeck,2))]; % make the deck deck = deck(randperm(length(deck))); % shuffle if(all(deck(deckCards(nDeck,:))==0)) % are all the same? rDecks(nDeck) = rDecks(nDeck) + 1; end end end rDecks = rDecks / nReps; disp([prod(1:7)/prod(15:21), rDecks(1)]); disp([prod(8:14)/prod(36:42), rDecks(2)]);

Riccardo FabrisPosted 7/24/12 12:30 AMCan you create the probability curves for less than 7 cards as well? if the probability can be placed in a curve it could be that we were both right, depending on what shape the two curves are at :P

Gabi TeodoruPosted 7/24/12 10:52 AMSure -- with fewer players, it is more likely to get a proportion of research cards in your hand that is close to the proportion of research cards in the deck. Blue is 3 players, Green is 6 players: 1/3 of the cards are research cards:

Riccardo FabrisPosted 7/24/12 1:34 PMOkay, cool to know. Seems you were right: higher number of players make it slightly more likely that you get more 'clumping' of cards. I was gonna say that the lower numbers for 0 to 2 cards show the opposite but considering the scenario, if you don't get the cards, someone else will, which is what we were discussing in the first place. Thanks for running the maths.