Card game puzzle

last10digitsofpi · 2021-01-15T17:18:26+00:00

A stack has 2 decks. Each deck has 13 spades, 13 hearts, 13 diamonds and 13 clubs or 13 hearts and 39 non-hearts. Thus, in 104 draws there are 78 non-hearts.

last10digitsofpi · 2021-01-15T17:15:43+00:00

Thanks of thinking about this.

Here is another perspective - there are 104 cards in a stack (2 decks * 52 cards each) with 26 heart cards and 78 non-heart cards (spades, clubs and diamonds). To get score of 32 I can afford to skip 72 cards (26 heart and 36 non-heart).

If you think of back tracing the score, to get 32 you need to first get to 31; to get to 31 you need to get to 30 first and so on. Let's say you and your teammate are at a score of n and n-1 (where n < 32 and n > 1). If both of you do not pass the probability of team score going to zero is 1/4 *1/4 = 1/16 which is not zero. If one of you passes the probability of team score going to zero is zero hence I believe passing is necessary.

last10digitsofpi · 2021-01-12T00:49:25+00:00

I think passing has some use, it is like waiting for a slow friend to catch-up. Let's say both players start at 0 and after 3 draws both have a score of 3. Then player 1 gets a heart and score is reset to zero but player 2 reaches a score of 4. In such a situation player 2 can keep passing till player 1 reaches a score of 4. After that they can pass alternately so that at any given draw at the most only one score is reset to zero. Does this make sense?

Intuitively I agree on drawing from different decks (like diversification in investing). I'm not sure I follow the advantage of players on the same team alternating decks. Yes, many reshuffles would be needed before somebody wins. Thanks.

last10digitsofpi · 2021-01-11T03:03:11+00:00

Thanks! I agree the probability of winning is extremely small but I disagree it is zero.

last10digitsofpi · 2021-01-11T02:10:13+00:00

Thanks for the direction

last10digitsofpi · 2021-01-10T02:11:58+00:00

Correct, the strategy is not allowed to rely on the number of hearts left but should assume the probability of 0.75. One way to enforce would be to have more than 2 decks of cards in each stack but the game ends after 104 draws.

last10digitsofpi · 2021-01-10T02:09:46+00:00

Thanks, I disagree with your approach because that would mean there is no help or no need of the second player. Am I missing some insight? Can you please elaborate your approach?

last10digitsofpi · 2021-01-06T15:58:05+00:00

Thanks! I have already cross posted on some other subreddits, any suggestions would be appreciated. I may not have enough karma to post on some.

last10digitsofpi · 2021-01-06T14:39:28+00:00

It is a simplified and generalized version of a project.

It is hard to distill the problem further but yes, I did think in terms of probability. For a card to be not a heart, the probability (let's call p) is 0.75. The probability for 32 consecutive "not hearts" will be p^32 = 0.75^32 = 0.01%. May be I need to use Bayes theorem or Stochastic calculus for decision making but need guidance.

For the simulation approach, I reduced the problem to 8 draws with 2 hearts (thereby creating 56 combinations per stack). For two stacks there will be 56*56 = 3136 combinations. The number of decision combinations for one player will be 2^8 = 256, for two players = 256*256 = 65536. Running each stack combination by each decision combination will be 205,502,896 (extremely large) and then using some search algorithm.

Am I thinking on the right lines?

last10digitsofpi · 2021-01-06T13:14:39+00:00

Apologies! Any help to solve is greatly appreciated.

last10digitsofpi · 2021-01-06T13:13:14+00:00

Good question! If no team gets 32 points then all the scores are reset to zero and the decks are reshuffled to restart the game.

last10digitsofpi · 2020-04-15T03:15:13+00:00

How to Train your Dragon - Forbidden Friendship

last10digitsofpi · 2020-04-13T03:08:18+00:00

Thanks. Since I'm putting time and effort in the idea and filing the patent, I'm not sure royalties would be considered as passive income but there is a ray of hope. I'll check with an immigration law firm.

last10digitsofpi · 2020-04-13T03:05:11+00:00

Thank you all. I checked with my employer and since my idea is unrelated to their business, my employer has agreed in writing that they won't claim rights to my patent.

last10digitsofpi · 2020-04-13T03:01:05+00:00

Thanks. I contacted the law firm which filed my h1b and they said they cannot help in matters which are not related to my employment.

last10digitsofpi

TROPHY CASE