Which game is smarter, poker or teen patti?
The Hollywood caper The Sting (1973) includes a memorable depiction of a poker game, in which a lot of cheating is going on. Cinema must, however, wait until we are done with the first puzzle of the day. This too is about poker, and the rules of the game now may help you warm up for The Sting later. In a poker game, every player is dealt a hand of five cards, and the strongest hand still in play wins. So which combination is stronger than the other? In poker’s ranking system, the strongest possible hand is a straight flush, in which all five cards are of the same suit, with their ranks in sequence. If two players hold a straight flush, the one with the higher top card wins. The above example of A-K-Q-J-10 is the strongest possible, also called a royal flush. It beats all other straight flush combinations, such as 9-8-7-6-5 of one suit. Again, 9-8-7-6-5 is better than 6-5-4-3-2. And so on. Next in the hierarchy is “four of a kind”, which needs no explanation. Four 10s (the fifth card can be anything) is a stronger hand than four 9s, for example, while four aces is even better. But each of these combinations would rank lower than a straight flush, irrespective of whether the cards in the straight flush were low or high. In India, there’s a card game similar to poker in some ways, yet different. Teen patti involves three cards per hand, compared to poker’s five. Also, while teen patti does not allow players to change any of the cards they have been dealt, poker gives them the option to discard cards and draw fresh ones. In teen patti, the strongest combination is taken as the “trio ”or“trail”. It means the player has three cards of the same rank, such as A-A-A or 7-7-7. The second-best combination is the straight flush (three cards in sequence, same suit).
#Puzzle 15.1
In poker, the straight flush’s top rank implies that it has a lower probability of appearing than four of a kind, which is ranked lower. On the other hand, in teen patti, the trio (three of a kind) ranks higher than a straight flush, which implies that the trio has a lower probability of appearing than a straight flush.
Is the ranking system flawed in one of the games, or both?
#Puzzle 15.2
In five-card draw poker, any player can, if they wish, discard one, two or three cards from their original five, and draw the top one, two or three cards (as the case may be) from the remainder of the deck. In the sequence from The Sting, the cards have been secretly set up by the cheat Doyle Lonnegan (Robert Shaw) so that each player gets a hand he has predetermined. Henry Gondorff (Paul Newman) has been dealt three 3s and two other cards, while Lonnegan has two 9s and three other cards. Hoping to improve his hand to four 3s, Henry discards a certain number of cards and draws the same number of cards from the top of the remaining 42 cards. Lonnegan, then, discards a certain number of cards and draws as many. Henry ends with four 3s and a fifth card, while Lonnegan’s final hand is four 9s and a fifth card. Exactly as Lonnegan had planned. But he wouldn’t have known beforehand whether Henry would decide to discard-and-draw one card or two cards.
After the first 10 cards had been dealt, in what order were the top few cards in the remainder of the deck arranged?