Draw a 7 cards out of a deck. Some cards have special properties. What are my odds of grabbing 6 specific cards on the first draw of 7 cards?

There 60 colored cards in a deck, within that deck there are 29 different colors of cards, meaning there are more than 1 of some the cards. I will write the amount of each colored card below. Some cards have special properties that allow you to draw several more cards if drawn or find a specific card with in the deck. If I were to shuffle the cards and to draw 7 cards, what are my odds of drawing a lime, amber, aqua, blue, and 2 green cards? How can I answer this in MATLAB?

• 1 Blonde
• 1 Snow
• 2 White
• 2 Grey
• 1 Silver *shuffle your hand into the deck, then flip a coin, if heads draw 7 cards, if tails draw 4 cards
• 1 Charcoal
• 3 Pink *discard your hand, then draw 7 cards.
• 1 Rose *search your deck for up to 2 green or 2 purple cards or 1 green and 1 purple card, then shuffle your deck
• 2 Folly
• 1 Red
• 1 Ruby
• 2 Rust
• 4 Brown *discard 2 cards from your hand, then search the deck for either an amber, aqua, or blue card, then shuffle the deck
• 3 Tan *look at the top 4 cards of the deck, if you find a silver, pink, rose, brown, orange, lime card there you may put it into your hand, then shuffle the deck
• 3 Wheat
• 1 Orange * search your deck for a silver, pink, rose, brown, orange, lime card and put it into your hand, then shuffle the deck
• 2 Gold
• 4 Amber
• 2 Yellow
• 3 Mustard
• 6 Green
• 3 Lime
• 1 Teal
• 2 Cyan
• 2 Aqua
• 2 Blue
• 1 Cobalt
• 2 Violet
• 1 Purple

[James Tursa]

What have you done so far? Please make an attempt and post your code, and ask specific questions about it that you need help with. Then we can comment on it and offer suggestions/corrections/improvements.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Walter Roberson]

If you draw 3 Pink the first time then you need to discard all of your cards and draw 7 new ones. If you get lime, amber, aqua, blue, and 2 green cards in that new draw, does it count as a successful draw of lime, amber, aqua, blue, and 2 green cards for the purpose of calculating odds?

Do you need to draw the 7 new cards if you get all 3 Pink, or do you need to draw the 7 new cards if you get even 1 Pink?

What about if you draw those 6 cards that are the target but you also draw 1 silver, which requires that you shuffle your hand in to the deck. Do you get to count success because you had the right cards before you had to shuffle your cards in? Do you only count success if you have the right set of cards after all necessary actions are taken?

If one of the cards in your hand has a special action requiring that you draw new cards, and the new cards you have require you to draw new cards, do you keep going obeying the instructions until you have a hand that has no more special actions?

What do you do if you draw multiple cards that indicate different actions? Is there a priority, such as having to start from the top of that list? What do you do if you draw multiple of the same special cards?

As you can see, you left a lot of questions undefined. You cannot successfully code your program until you know what to do in each case.

[Alex Simmons]

all special conditions are optional, you do not have to invoke them if you do not wish to. if a situation like that happens, the code would run variation of choosing to invoke the condition and another would choose not to. which ever one got closer to the goal, would be the one that the code would proceed with.

[Walter Roberson]

When you run a Monte Carlo simulation and there is a choice of actions, you would normally choose one of the actions randomly and proceed with it.

If you instead run all of the actions simultaneously and one or more of the actions involve probability (dealing new cards) then you need to merge the probabilities associated with all of the possibilities in order to get an overall probability. But in order to do that, you need to know how to weight the various branches. Because a person "playing the game" would not be able to select all of the actions simultaneously, you would normally weight the branches by the conditional probability that the person selected the branch. And if you are going to do that then you might as well just select one branch at random and "play it out" rather than running all of the branches simultaneously.

You need to decide whether you are doing a Monte Carlo simulation, in which case you need to choose possibilities randomly, or if you are exploring the entire state space of all of the possible games to find the absolute probability of winning, or if you are doing something like an Alpha-Beta pruning to try to find winning strategies (like you would if you were exploring a chess or checkers game.)

Answer 1

[Image Analyst]

You can assign certain ID numbers to the cards, like gold cards are card 1 & 2, and amber cards are 3,4,5 & 6, and so on for the other colors. Then use randperm to shuffle, and then use indexing to deal cards from the deck. It's not too hard. See my attached demos.

Sounds like homework, so I think my demos are help enough. If it's homework, you're supposed to attach a tag of "homework" to your post.

[Alex Simmons]

no its not homework. its a application to another program. I used colors to try and simplify things where i could. The idea of indexing is really good. I will try it out and post the results. thank you.

[Alex Simmons]

clc; clear;
%Deck
deck={'blonde' 'snow' 'white' 'white' 'grey' 'grey' 'silver' 'charcoal' 'pink' 'pink' 'pink' 'rose' 'folly' 'folly' 'red' 'ruby' 'rust' 'rust' 'brown' 'brown' 'brown' 'brown' 'tan' 'tan' 'tan' 'wheat' 'wheat' 'wheat' 'orange' 'gold' 'gold' 'amber' 'amber' 'amber' 'amber' 'yellow' 'yellow' 'mustard' 'mustard' 'mustard' 'green' 'green' 'green' 'green' 'green' 'green' 'lime' 'lime' 'lime' 'teal' 'cyan' 'cyan' 'aqua' 'aqua' 'blue' 'blue' 'cobalt' 'violet' 'violet' 'purple'};

%Hand
hand=randsample(deck,7,false)

this is what i got so far, how do check my hand, to see if any of the cards have a special condition, and use or not use the special condition?

[Image Analyst]

Check out Walter's code - it looks pretty well fleshed out.

Answer 2

[Walter Roberson]

cards = {'blonde', 1;
        'snow', 1;
        'white', 2;
        'grey', 2;
        'silver', 1;
        'charcoal', 1;
        'pink', 3;
        'rose', 1;
        'folly', 2;
        'red', 1;
        'ruby', 1;
        'rust', 2;
        'brown', 4;
        'tan', 3;
        'wheat', 3;
        'orange',  1;
        'gold', 2;
        'amber', 4;
        'yellow', 2;
        'mustard', 3;
        'green', 6;
        'lime', 3;
        'teal', 1;
        'cyan', 2; 
        'aqua', 2;
        'blue', 2;
        'cobalt', 1;
        'violet', 2;
        'purple', 1};

special_cards = {'silver', 'pink', 'rose', 'brown', 'tan', 'orange'}

numcolor = size(cards,1);

cards = [cards, repmat({false}, numcolor, 1)];
[~, idx] = ismember(special_cards, cards(:,1) );
cards(idx,3) = {true};

At this point, cards is a cell array whose first column is a color, second column is a repeat count, and third column is true if the color is special.

card_idx = [];
for K = 1 : numcolor
  card_idx = [card_idx, repmat(K, 1, cards{K,2})];
end

name_this_card = @(idx) [cards{card_idx(idx),1}, repmat('*',1,cards{card_idx(idx),3})]
name_cards = @(card_id_list) arrayfun(name_this_card, card_id_list, 'Uniform', 0);

Now card_idx is a "population" of cards that can be sampled from, with the result indicating which row of "cards" the card corresponds to. name_this_card is a helper function and name_cards is a function to name the cards in a list.

To draw cards:

num_cards_in_deck = length(card_idx);

deck_discards = [];
deck_remaining = randperm(num_cards_in_deck);
cards_in_hand = [];

then

num_to_draw = 7;     %this time

cards_drawn = deck_remaining(1:num_to_draw);
deck_remaining = deck_remaining(num_to_draw+1:end);
cards_in_hand = [cards_in_hand, cards_drawn];

named_hand = name_cards(cards_in_hand);

fprintf('You now have:');
fprintf(' %s', named_hand{:});
fprintf('\n');

[Alex Simmons]

this is cool. working on if then statements to see if there are any special cards in the hand, and how to use them if need be. will post my results soon.

[Walter Roberson]

which_are_special = [cards{card_idx(cards_in_hand),3}];

Now it is a logical vector of whether each card in the hand is special.

(Did you notice that I put a '*' beside the names of the cards that are special in the hand printout? )

Answer 3

[Alex Simmons]

well i was thinking along the lines of something like spc_pink=strfind(named_hand,'pink*'); which returns logical values in a array if true. then use the logical value to execute the special condition. for instance if pink is drawn the player has the option to discard the hand and redraw 7 new cards.

[Walter Roberson]

By the way if you do not want the * in the name of the special cards, change

name_this_card = @(idx) [cards{card_idx(idx),1}, repmat('*',1,cards{card_idx(idx),3})];

to

name_this_card = @(idx) cards{card_idx(idx),1};

[Alex Simmons]

ok thx

[Alex Simmons]

i noticed you created a discard array, how do I send cards there if I wanted to discard and redraw a hand?

[Walter Roberson]

discard_which = [1 4 5];   %for example
cards_being_discarded = cards_in_hand(discard_which);
cards_in_hand(discard_which) = [];
discard_deck = [discard_deck, cards_being_discarded];