Sunday, September 26, 2021

# Games Bond returns with Problematics and Teen Patti

## You saw Bond winning at Chemin-de-fer and Poker. Let's teach him Teen Patti now.

Bond plays Chemin-de-fer in ‘Dr No’ and Poker in ‘Casino Royale’. (Source: Video grabs)

For the dedicated readers who kept this blog going for 25 consecutive weeks, an explanation is in order. You will demand to know where we have been, Problematics and I. The long break was induced by a brief illness followed by a prolonged loss of momentum, coupled with tiredness during a Bihar election that brought a lot of work to journalists. So, with apologies for having kept you waiting so long, welcome to Problematics Season 2 Episode 1. ‘Spectre’, the newest Bond film, has no gambling but Bond and gambling are as timeless as this puzzle. Bond’s very first appearance on screen, in fact, is at a casino, where he is winning at Chemin-de-fer, a game whose rules I am not fully familiar with. His last appearance at a casino, on the other hand, features a game of Poker, whose rules are an extension of India’s own Teen Patti.

For those new to one or both of these games, Poker is played with five cards per player, and Teen Patti with three per player. The rules for placing the bets are very elaborate, particularly in Poker, but the basic idea in both games is that the winner is the player who holds the best combination of cards. To know which combination is “better” than another, there is a ranking system in each game:

* A “straight flush”, the best possible hand in Poker, is the sequence 10-J-Q-K-A with all five cards belonging to the same suit (e.g. diamonds, as illustrated).
* A “straight” in Poker or a “run” in Teen Patti means the cards are in sequence (e.g. 2-3-4-5-6 in Poker), but not all belong to the same suit.
* In a “flush” in either game, all the cards belong to the same suit, but not all pip values are in sequence.
* Some combinations are self-explanatory — “four of a kind”, “trio”, “two pair”, “pair”.
* A “full house” in Poker means three cards of one value and two of another (see example).
* Finally, a “high card” means the cards don’t fit into any of the other combinations; the highest card determines the winner.

So what is the basis of these rankings? The less likely you are to get a particular combination, the higher it is placed in the pecking order. A trio in Teen Patti, for example, is less likely to be dealt to you than, say, a pair. That is the way things should have been, in any case.

The creators goofed at one point, you see. It is surprising how many experienced players have no idea that there is a fundamental flaw in one of these two games. If you take both games and examine the probabilities of each combination being dealt to a player from a pack of 52 cards, you will find that in one game, one more likely combination is ranked higher than another, less likely one.

Puzzle#26A: Which game has the flaw? And if Bond the probability theorist were to alter the rules, he would swap which two combinations in the ranking order?

Puzzle#26B: The easier puzzle is briefly said. First Sarojini Naidu and later Lata Mangeshkar have been described as the “Nightingale of India” for their voice, besides their poetry and music. The sobriquet is well meaning but scientifically misplaced. Agree, disagree?

What you wrote

It’s been 3½ months since the last set of puzzles came out, so here’s a recap. On two different days, the dollar exchange for Rs 10,000 was two different amounts, for which certain conditions were specified. The second puzzle was from Lewis Carroll, who had spotted an interesting trend with pounds, shillings and pence.
Dear Kabir — I found the first problem (Puzzle#25A) easy. The answer is \$156.75 and \$150.39. If dollars were x and cents were y, then y – x/4 = 36 and x – 2y = 6. Just solved this to obtain the values for x and y. If this had not worked, would have tried y – (1 + x/4) = 36 and x – (2y – 1) = 5, taking into account that y – x/4 could be of negative value. But the first set of equations worked and got the answers.
— Sanjay Gupta (New Delhi).
***
Dear Kabir — In Puzzle# 25B, let us put down ‘x’ pounds ‘y’ shillings ‘z’ pence. My solution is attached.
— Anirudha Hulsurkar (IIT Roorkee)