Probability: The chances of how likely something will turn (in games, choices, events, etc.)
Observed Probability: A probability of an event that is calculated through data that has been observed. Theoretical Probability: A probability of an event that is calculated through how we expect an event to happen. Conditional Probability: A probability of an event [A] that is calculated given that another event [B] has already happened. Probability of Multiple Events: The chances of different events occurring calculated through additional individual or conditional probabilities multiplied by the probability of the first event. Expected Value: A predicted outcome of an event(s) that is calculated by all possible possibilities of an event happened multiplied by the number of times the event happens. Two-Way Table: A table that separates data into two distinguishable variables and totals, which are labeled joint and marginal probability outcomes respectively, it's very helpful for finding joint and conditional probabilities. Tree Diagram: A diagram that branches out with the different probabilities of an event, it's also helpful for joint and conditional probabilities. Joint Probability: The probability of two events happening at the same time or together, the formula being Pr[A and B]= P[A | B] * P[B] Marginal Probability: The probability of an event happening, regardless of a condition, usually seen as Pr[A] or Pr[B]. |
The slideshow above shows example of some of the terms/definitions on the left. It goes as shown, Tree diagram (1st picture), Two-Way Tables (2nd picture), and Joint/Marginal Probabilities in a Two-Way Table (3rd picture)
|
|
With my partner, Nia Asbill, we chose to play a 2-9 player card game called 31/Thirty in One, any and all pictures will be included below. Its exact date of creation is unknown, but some of its origins go back to around 1440 in one of Bernadine of Siena's speeches. It was most popular in Spain, but there have been many different variations of the game around Europe and Asia. Some would say that 31 is the predecessor of 21/Blackjack, the similarities being that to win you need to reach a certain value, and you add onto your hand with more/different cards. Their difference being the value to win (31 and 21 respectively) and that 31 is a draw-and-discard game, where you keep the same amount of cards the whole game.
|
Since the cards slowly decrease by 2 as they're being dealt, it would mean that the denominator for the probabilities would also decrease by 2 after the first event. which in this example gives the two 10 value cards a larger chance to be in the same hand as the Ace in the first event. For the In my game, probability comes into hand through the number of players, how the cards are dealt, what suit players choose to go with, as well as so many other possibilities. One of the ways to win is to have a winning hand of 31 with the same suit (hearts, diamonds, clubs, and spades), which got me wondering. What is the probability of being dealt a winning hand of 31 in one suit?
It's a lot harder for me to calculate the probability of getting a winning hand with a lot of players so to keep it simple, I used two players (which I forgot to mention in the calculations on the right). Anyways, the only way to get the value of exactly 31 is to have an Ace and two 10 value cards (Ace being 11, so it would be 11+10+10=31). For a single suit, there is one Ace and 4 possible 10 value cards, and a whole deck consists of 52 cards. When dealing 3 cards to each player--in this case two players--the 52 cards will go down to 46 cards, which means that there is a chance that the cards we're looking for are in those 6 cards that the dealer dealt to the players. |