Part 1 |
In this project, we were taught probability. This began with a simple game called pig. In this game you roll a dice and you continue rolling until you stop or it lands on a 1. The goal was to reach 50 points and if the di landed on 1, you lost all your points for that roll. This game tasked us to find the best strategy and to observe the probability of it landing on a 1 after so many rolls. We later moved onto other dice games where we observed the probability of rolling a specific number using two dice. Then we went into worksheets like who's cheating and my dog ate my homework. These introduced us to theoretical probability and observed probability. Theoretical probability is the calculated chance of something happening, or the probability on paper. Observed is the actual probability that you have observed from the set of data from the experiment. This worksheets we did after this focused on probability trees. These helped us stay organized when learning about probability of multiple outcomes and showed us the conditional probability of something happening. Conditional probability is the probability that A happens given that B occurred. The branches in the tree showed the probability of the multiple outcomes in each branch. Then this transitions into expected value which you find by multiplying all the the probabilities of multiple outcomes together. We did more worksheets after this were focused on 2 way table, marginal probability, and joint probability. Two way tables have two probabilities that are dependent. Joint probability is the probability of something happening at the same time as another outcome. This would be like choosing a girl out of any amount of people who is also wearing green. The last thing we covered was marginal probability. Marginal probability is the probability of one event where multiple events are supplied.
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Part 2: Bassetta
Origin: Bassetta originated in Renaissance Italy, was 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. Because Bassetta has huge potential losses, 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.
Who played it/ where was it played: Bassetta was played by anyone who had the funds to originally, but was causing so many ot fall into debt it was soon only limited to greeter families. This game was traditionally playing in homes in Italy.
Modern Version: Bassetta is still played to this day, however it was the precursor to it's modern day adaptation, poker.
Gameplay: 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.
How does chance play into this?
Because this is based on random cards and you don’t know which card comes up next, this is a game of chance.
Who played it/ where was it played: Bassetta was played by anyone who had the funds to originally, but was causing so many ot fall into debt it was soon only limited to greeter families. This game was traditionally playing in homes in Italy.
Modern Version: Bassetta is still played to this day, however it was the precursor to it's modern day adaptation, poker.
Gameplay: 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.
How does chance play into this?
Because this is based on random cards and you don’t know which card comes up next, this is a game of chance.
Part 3
Above is Basseta in the Renaissance
Question this is addressing: What is the probability of peroliing all 4 times?
Because of the way the game is played, itś very unlikely, yet very beneficial, to have your card pulled by the dealer 4 times, as a win card. Aside are photos of our tree diagram and calculations to figure out the probability of this. To the right is a photo of the cards that we created. These are based off of original Bassetta cards. We printed them on card stock and laminated them. |
Habits of a Mathematician
In making these calculations, we used habits of a mathematician. One such habit would be staying organized. As you can see, we kept our probability calculations organized with a probability tree. This helps us follow and visualize what is really going on each time a card is pulled. Another such habit is starting small. We went back to the start and began solving the probability of winning all 4 times with the first card drawn. Then we worked our way up each branch of the tree until we finally came to our conclusion. |
Part 4: Reflection
Overall this project ran pretty smoothly. At first it was a struggle to fully grasp the rules of our game, but we eventually got a firm enough understanding to present it to Mr. Pringle. We still needed some practice even after that but in the end the game seemed simple.It was also a bit of a challenge to find historical information on the game of Basstta. It took some digging but I found some great information that helped me to understand how the game came about and why it was so favorable for gambling. As we found out in our calculations the odds are extremely low for winning all 4 times, but the payout is so big that it was worth the risk. I was proud with how the cards that we made for the game turned out, and although they may look simple, a lot of work as put into sizing and scaling. An issue we ran into with them though was that not all the details were printed to we had to fill the cards in with sharpie. The final product of our game and calculations turned out really well in my eyes and I'm satisfied with the results.