Last week’s building distribution problem is best solved physically, by placing moving pieces on a board, as proposed by the Alquerque Group in Seville. Here is the solution sent by Salva Fuster:
The multicolored cuboids of different heights, by the way, come from the MMACA (Museum of Mathematics of Catalonia), based in the Palau Mercader de CornellĂ , a must-see for those who come there.
Some poker hands
An apparently trivial problem about the probability that by picking up the top card of a French deck (52 cards, 26 red and 26 black) we win a bet, sparked a wide debate (see last week’s comments) that reminds us, once more, how elusive these types of problems can be.
And speaking of cards and bets, the calculation of probabilities, in addition to being elusive, is very important when playing, for example, some poker hands. So let’s move mentally to a typical living room of the Wild West to deal with some of the problems that can arise throughout a game (it is supposed to be played with a full deck and without jokers).
Let’s start at the beginning: as is well known, after one player shuffles the cards, another player cuts the deck into two piles. What is the probability that both piles are the same? And what about one lot being twice the other? And the rigorous meta-problem: do the mathematically calculated probabilities fully reflect reality in this case, or in practice are the requested probabilities substantially different?
After cutting and dealing, you are dealt a very interesting hand: an ace of clubs and four hearts: 7, 8, 10 and ace. You have two options: keep the two aces and ask for three cards or keep the four hearts and ask for a flush. What would you do and why?
Same hand, but now you can see out of the corner of your eye that your partner on the right has the ace of diamonds and a pair of hearts. Does this change your decision?
Same hand. Now you don’t see your neighbor’s cards, but the one who has dealt them is the famous gambler John Ace in the Sleeve Morgan, who one out of every two times he deals manages to get an ace up his sleeve without anyone noticing. What do you do in this case?
I suggest that you first answer intuitively and then calculate the probabilities relative to each option.
And to gauge your intuition pokeristics You can start with this quick test:
1. The probability of getting a poker served is approximately:
a) One in a million.
b) One in fifty thousand.
c) One in five thousand.
2. The probability of getting a pocket of aces served is approximately:
a) One in a million.
b) One in a hundred thousand.
c) One in fifty thousand.
3. The probability of drawing a full house of aces and tens is approximately:
a) One in a hundred thousand.
b) One in fifty thousand.
c) One in ten thousand.
4. The probability that there is at least one ace in the dealt hand (and provided you do not deal the cards Ace in the Sleeve Morgan) is approximately:
a) One in ten.
b) One in five.
c) One out of three.
In all cases it is assumed that the game is played with the full deck and without jokers.
Carlo Frabetti is a writer and mathematician, member of the New York Academy of Sciences. He has published more than 50 popular science works for adults, children and young people, including ‘Damn Physics’, ‘Damn Mathematics’ or ‘The Great Game’. He was a screenwriter for ‘The Crystal Ball’.
You can follow MATTER on Facebook, Twitter and Instagramor sign up here to receive our weekly newsletter.
#saloon #math