Probability: The measurement of the likelihood an event will happen.
Observed Probability: A variable that is observed and dictates the outcome.
Theoretical Probability: Or expected probability, an example would be if you throw a penny the probability of getting heads is 1/2 and tails is 1/2.
Conditional Probability: Probability of an event, given that another event has already occurred.
Probability of Multiple Events: The probability of many events can be calculated by multiplying their independent properties together.For example finding the probability of getting heads three times in coin tosses. 1/2 * 1/2 * 1/2 = 1/8
Expected Value: A predicted value of a variable.
Two-Way Tables: A table that organizes data about two variables; usually helpful getting data onto paper.
Tree Diagram: A diagram with a structure of branches connecting lines, representing different processes, relationships and outcomes. Another way to get data onto paper to help with calculations
Joint Probability: A statistical measure where the likelihood of two events happening together and at the same point and at the same point in time are calculated. For example, the probability of event Y happening at the same time as event X.
Marginal Probability: The probability of one variable taking a specific value irrespective of the values of the others.
Origin: Bassetta emerged in Renaissance Italy, was later introduced to France, and then slowly found it’s way to England. Beginning of play in Italy was circa 1500 and wasn’t recorded in England until around 1700. Bassetta has potential for huge losses(although there is also a small window for large winnings), France declared an edict that only “sons of great families” could be a talliere. Lower classes were also prevented from gambling more than a certain amount. However, even with the edict in place, several families fell into financial ruin resulting in the games ban by Louis XIV in 1691. today the game has lost its touch, only played in history.
How It is played: I chose this card game mostly because it looked so complicated and outlandish. I wanted to take a challenge in this project because card games interest me. at first I had little ideas how to even breakdown the games instructions, but I showed one aspect of a mathematician by acting out the problem, putting it in front of me. I got two decks of cards and followed the steps while actually playing with my cards and invisible opponents. Enjoy reading about how to actually play Bassetta, I hope you can follow along.
To play there’s a dealer (talliere) who gets their own full deck of cards and then depending on how many players (punters) there are, a varying number of additional decks is used (1 deck for 2 to 3 players, 2 decks for 4 to 7, etc), the decks are divided into their suits -13 cards in all- and called a book.
The player then decides which of their cards they would like to play and places them face up on the table; bets are made by placing a wager on top of any upturned card and all cards in a book can be bet on with any wager each turn.
Once all bets have been made the dealer turns over one card face up from the bottom of their full deck and wins all bets placed on cards that match this one's rank.
Then the dealer deals two cards off the top of the deck -first card wins, second card loses- meaning that if the player's card matches the rank of the second card then the dealer takes their wager and that card is out of play for this round, but if the player's card matched the rank of the first card, the dealer pays out a match of the wager on the player's card.
From here the player can either retire the card and keep the wager won or leave the card and wager in play skort of like double or nothing. This is called a peroli and the card is marked to signify this (usually the corner is folded).
If a card is perolied and i️t loses the dealer takes the original wager and the card is taken out of play, but if i️t wins the wager is paid to the player at 7 times the original wager, this is called winning a Sept & Leva. This can be taken out of play or left in play the same as the first peroli.
A player can peroli a card up to 4 times (4 corners).
The next peroli is called Quinze & Leva—15 times the initial wager, the third is called Trente & Leva—30 times the initial wager, and the fourth peroli is called Soixante & Leva—60 times the initial wager.
If a perolied card loses at any point the player only loses the initial wager.
The dealer's final card is a losing card and if a player's card matches its rank the wager goes to the dealer.
Chance and probability play huge roles in most card games, and especially this one. Every time you draw a card the probability that that card will show up will be less and less. there is a constant chance that you will loose or win a hand that is determined by the one card drawn from the deck.
Observed Probability: A variable that is observed and dictates the outcome.
Theoretical Probability: Or expected probability, an example would be if you throw a penny the probability of getting heads is 1/2 and tails is 1/2.
Conditional Probability: Probability of an event, given that another event has already occurred.
Probability of Multiple Events: The probability of many events can be calculated by multiplying their independent properties together.For example finding the probability of getting heads three times in coin tosses. 1/2 * 1/2 * 1/2 = 1/8
Expected Value: A predicted value of a variable.
Two-Way Tables: A table that organizes data about two variables; usually helpful getting data onto paper.
Tree Diagram: A diagram with a structure of branches connecting lines, representing different processes, relationships and outcomes. Another way to get data onto paper to help with calculations
Joint Probability: A statistical measure where the likelihood of two events happening together and at the same point and at the same point in time are calculated. For example, the probability of event Y happening at the same time as event X.
Marginal Probability: The probability of one variable taking a specific value irrespective of the values of the others.
Origin: Bassetta emerged in Renaissance Italy, was later introduced to France, and then slowly found it’s way to England. Beginning of play in Italy was circa 1500 and wasn’t recorded in England until around 1700. Bassetta has potential for huge losses(although there is also a small window for large winnings), France declared an edict that only “sons of great families” could be a talliere. Lower classes were also prevented from gambling more than a certain amount. However, even with the edict in place, several families fell into financial ruin resulting in the games ban by Louis XIV in 1691. today the game has lost its touch, only played in history.
How It is played: I chose this card game mostly because it looked so complicated and outlandish. I wanted to take a challenge in this project because card games interest me. at first I had little ideas how to even breakdown the games instructions, but I showed one aspect of a mathematician by acting out the problem, putting it in front of me. I got two decks of cards and followed the steps while actually playing with my cards and invisible opponents. Enjoy reading about how to actually play Bassetta, I hope you can follow along.
To play there’s a dealer (talliere) who gets their own full deck of cards and then depending on how many players (punters) there are, a varying number of additional decks is used (1 deck for 2 to 3 players, 2 decks for 4 to 7, etc), the decks are divided into their suits -13 cards in all- and called a book.
The player then decides which of their cards they would like to play and places them face up on the table; bets are made by placing a wager on top of any upturned card and all cards in a book can be bet on with any wager each turn.
Once all bets have been made the dealer turns over one card face up from the bottom of their full deck and wins all bets placed on cards that match this one's rank.
Then the dealer deals two cards off the top of the deck -first card wins, second card loses- meaning that if the player's card matches the rank of the second card then the dealer takes their wager and that card is out of play for this round, but if the player's card matched the rank of the first card, the dealer pays out a match of the wager on the player's card.
From here the player can either retire the card and keep the wager won or leave the card and wager in play skort of like double or nothing. This is called a peroli and the card is marked to signify this (usually the corner is folded).
If a card is perolied and i️t loses the dealer takes the original wager and the card is taken out of play, but if i️t wins the wager is paid to the player at 7 times the original wager, this is called winning a Sept & Leva. This can be taken out of play or left in play the same as the first peroli.
A player can peroli a card up to 4 times (4 corners).
The next peroli is called Quinze & Leva—15 times the initial wager, the third is called Trente & Leva—30 times the initial wager, and the fourth peroli is called Soixante & Leva—60 times the initial wager.
If a perolied card loses at any point the player only loses the initial wager.
The dealer's final card is a losing card and if a player's card matches its rank the wager goes to the dealer.
Chance and probability play huge roles in most card games, and especially this one. Every time you draw a card the probability that that card will show up will be less and less. there is a constant chance that you will loose or win a hand that is determined by the one card drawn from the deck.
Probability Analysis
The photos below show a probability tree (on the Left) and the probability calculations for four perolies(right). Again, perolies are the bets that have won a hand multiple times, but only can win 4 times. That is the maximum amount of times you can win one hand. The table shows one side starting with 4 cards out of 52, and the otherside with 48 cards out of 52. These resemble the 4 cards needed to get 4 wins and the 48 other cards that will need to be drawn during the loosing card from the dealer.
Habits of a Mathematician
Habits of a Mathematician help to problem solve in most mathematical situations and during Math Class I showed some of these aspects. I uses three of the habits of mathematicians when working of my probability analysis. I made a table, the probability tree, I drew a picture to better understand the calculations I needed to find the probabilities, and I acted out the problem by using two decks of cards to help with my understanding of the ways I would calculate. It was confusing to calculate because when making the table every time a card was withdrawn from the deck. |
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This was a suit of cards that some partners and I made using adobe illustrator. They were made to show what a suit of cards could of looked like in the time the game was payed ------> This is am example of how the cards used for Bassetta would look like in Italy. The cards were made fairly well because, most of the time, only the rich world play this game. |
Reflection
In my experience I feel like I worked hard this project, but I didn't really learn that much new. There wasn't much that I didn't understand because most of the things we worked on were review for me. I was working all of the time but it was mostly busy work for me and because of this I wasn't able to take up any challenge sheets. I often found myself doing challenge options on worksheets, but most of the time they weren't hard. I one thing that went really well for me was being able to understand the different probabilities given that another probability was involved. Usually it is very hard for me to dissect word problems, but for this, the different terms seemed to click for me. If I look back I see myself enacting many of the habits of a mathematician because many of the tactics for successful problem solving in math come naturally to me form practice. I often write out the problem and try to make connections to the real world by acting it out, starting simple to try and understand the whole question, and guessing and checking If I'm not sure how to solve a problem. To continue growing as a mathematician I am taking the next level of math at Palomar College. The last class I took was very informative and helped me learn many new concepts; I hope this next semester I will learn just as much.