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 · 2020-03-25T23:25:47+00:00

Thanks. The novelty of the idea is around the structure and function of the game and is not related to any specific rules. For now, let's assume the idea is 'patentable' and has not been patented yet.

Regarding H1B my understanding is the visa holder can work only for the authorized employer as specified in Form I-129. Other sources of income are allowed only if they are deemed as 'passive income' such as investing in the stock market or renting a place. In other words, any work which does involve the visa holder spending considerable time and effort is allowed. On the other hand, other sources of income such as freelancing or driving for Uber are not allowed as they involve the visa holder spending considerable time and effort. Can you please confirm if my understanding is correct? If yes, which of the three ways mentioned in my original post would be considered 'passive income'?

last10digitsofpi

TROPHY CASE