Counterfeiting


[SS] “Do you guys know the counterfeit coins puzzle?” Stan the Stat surveyed the table.

[LL] “Do you mean the 9 coin puzzle with two weighings or the 12 coin puzzle with three weighings?” Leroy the Lion countered.

[SS] “Good, then you’re ready for my new, poker-themed puzzle.”

[LL] “Fire away.”

[SS] “Okay. At a tournament, there was a problem with these very poker chips in front of us. Some immoral rodent snuck a counterfeit chip into circulation. Fortunately, we know the fake is one of these 14 chips (don’t ask how), and we were able to determine (ditto) that the fake chip weighed a different amount than the real chips. Unfortunately, our bathroom scale isn’t accurate enough to weigh the chips, but we dug out this old swing arm balance for you. Because we don’t have time for you to weigh each chip against every other one because I spent all our time laying out the puzzle, you only get three weighings to find the counterfeit chip. Can you do it?”

[LL] “That’s impossible. It took three weighings just to find the fake among a dozen; how can we find one among fourteen?”

[SS] “I assure you that it can be done. Maybe Figaro can help you out?”

[LL] “Need to think outside the box?”

[SS] “Perhaps.”

[FF] “Well, how do you solve the nine coin problem?” Figaro inquired.

[LL] “Not much of a challenge. In that puzzle you know that the fake coin is light. You just weigh any three against any other three. If they match, the fake is in the three you didn’t weigh; otherwise it’s one of the light three. Weigh any two of those three against each other, and you have your answer.”

[FF] “And the twelve coin problem?”

[LL] “That’s a bit harder, partly because you don’t know if the odd coin is lighter or heavier. I don’t remember the exact sequence, but you start by weighing any four against any other four.”

[FF] “So you eliminate eight of the twelve coins on the first weighing.”

[LL] “Right. The next step involves reusing some of the coins that you know are real, but I’d have to figure out the different cases.”

[RR] “What if Leroy pointed you to Figaro not because he’s an independent thinker, although that’s certainly true, but because he was playing with these other, presumably genuine, chips?” Roderick the Rock enjoined. “What if we add a known real poker chip to the mix and start by weighing five against five?”

{ highlight the following spoiler to read it }


[LL] “That’s it! If they balance, it’s easy. You can weigh three of the remaining chips against three that balanced. If those balance, you weigh either of the remaining chips. If they don’t, you know which way the pans tilted and you’ve narrowed it down to three chip, and you have the second half of the 9 coin problem.

If the first weighing doesn’t balance, weigh two from the light side (whichever the original real chip wasn’t on, that is) and one from the heavy side against two from the light side and one from the heavy side. If those match, you have two potential heavy chips and one potential light chip left, and you weigh one heavy and one light against two real chips. If those don’t match, then you’re down to the heavy chip on the heavy side and the two light chips on the lighter side, and you have a similar case.”1

[SS] “Very well done! Do you guys remember a couple years ago when a cheater tried to dispose of some fake poker chips in the toilet and got caught?”

[LL] “It wasn’t even the casino he was stealing from!”

[SS] “Right. That and three other recent incidents caught my attention for the combination of greed and idiocy:

  • In June 2013, Rear Admiral Timothy M. Giardina was caught using fake $500 poker chips at a Nebraska casino. Apparently the Navy officer, who had previously been banned from other casinos in Iowa and Kansas, was addicted to not only gambling but nicotine; he was caught on surveillance video taking cigarette butts out of an ash tray and smoking them. The Navy stripped him of a star, but no criminal charges were pressed.
  • In January 2014, Christian Lusardi introduced some fake poker chips at a Borgata poker tournament but got caught when he tried to flush $2.7 million worth of chips down the toilet at the nearby Harrah’s Resort and Casino and clogged the plumbing. The North Carolinian was sentenced to five years in prison.
  • Later in the same month, Rosa A. Nguyen and Vuong Q. Truong used fake $100 poker chips in the Maryland Live Casino then tried to dispose of unused fakes in Lake Accotink near their home in Springfield, Virginia. Only problem: the chips floated.
  • In December 2015, Sajid Rashid and Qamar Hussain were sentenced to 30 months in jail in Monte Carlo for marking up €10 chips up as &euro1,000 chips and collecting almost £s;3 million playing roulette. Their accomplice Zahidul Haque Khan got 10 months for accepting their loot. The British trio had made many visits to Monaco and had even been comped by the casino for their high rolling ways. Rashid had already served 14 months in jail and had been banned for life from British casinos.”

[LL] “I’d think that counterfeit poker chips are becoming less of a problem as casinos have begun using RFID2 technology, especially in larger denomination chips.”

[SS] “But even as casinos step up their security measures, you can never be safe from counterfeiting any time you play Hold ‘Em!”

[RR] “Ha ha. You mean like when your hole cards are counterfeited?”

[SS] “Indeed. “There’s no real consensus on what constitutes counterfeiting and what doesn’t, so I break things into three categories: Definitely, Borderline, and Not Counterfeiting:

Definitely Counterfeiting

Hand Opp. Flop Turn River Description
7♣7♦ A♣K♦ Q♥T♠T♣ 3♦ Q♠ Pocket pair counterfeited by higher two pairs on board (making 3 pairs)
7♣7♦ A♣K♦ Q♥Q♠7♥ Q♦ 7♠ Full house on flop counterfeited for half pot on river
7♣7♦ A♣K♦ Q♥Q♠T♣ Q♦ T♥ Full house on turn counterfeited for half pot
7♣7♦ A♣K♦ Q♥Q♠7♥ Q♦ Q♣ Full house on flop counterfeited for full pot when pocket pair becomes bad kicker
K♣Q♦ A♣K♦ J♥T♠9♣ Q♦ Straight counterfeited by turn giving opponent a higher straight
K♣Q♦ K♦2♣ J♥T♠9♣ Q♦ Straight counterfeited for half the pot
9♣8♦ any K♥K♠8♥ 8♣ K♦ River makes bigger full house on board, costing half a pot to most hands and losing to pocket Nines and higher
9♣8♦ any K♥K♠8♥ K♦ 8♣ Same as above but perhaps more painfully (but always behind pocket Nines in this case)
9♣8♦ T♣T♦ 9♥8♠2♣ 2♠ Two pairs counterfeited by pair on board, giving opponent a higher two pairs
9♣8♦ 9♥2♠ Q♥J♠8♣ J♥ 9♠ River improved hand to better two pairs yet cost half a pot (the dreaded 3 pairs again)
9♣8♦ A♣K♦ Q♣Q♦Q♥ 9♦ Q♠ Full house counterfeited for full pot when board makes four of a kind

Borderline Counterfeiting

Hand Opp. Flop Turn River Description
A♣K♦ 9♣8♦ Q♥T♠T♣ Q♦ Q♣ As of the turn, the Ace kicker was beating the Nine kicker, but the boat on the river removed the kicker from the picture
9♣8♣ A♣K♦ J♣5♣2♣ Q♣ Lower suited hole cards needing only three of the suit on the board can lose to a fourth suited card on the turn or river
9♣8♦ A♣9♦ J♠8♥5♠ J♥ 9♠ The Nine on the turn didn’t counterfeit the 98 because it was still ahead then! The 98 then improved on the river but lost.
7♣7♦ K♦2♣ 9♥8♠7♥ 6♣ 5♦ The set of Sevens was ahead until the straight on the board chopped the pot on the river; a flush on the board is even less likely to be considered counterfeiting (could have been behind on the flop or turn)

Not Counterfeiting

Hand Opp. Flop Turn River Description
9♣8♦ J♥T♥ T♠9♥8♥ J♠ It’s not counterfeiting if an opponent’s hand simply improves to beat you (like a Heart, Queen, Jack, Ten, or Seven on the turn here)
7♣7♦ A♣K♦ K♥Q♠7♥ Q♦ K♣ A Queen on the river is more obviously counterfeiting, but a King is just a bad beat

[LL] “That’s a lot of counterfeiting!”

[SS] “And that’s not even counting my kitchen renovation…”

Footnotes:

  1. Original puzzle posed by Biotop on the Straight Dope message board on June 9, 2010.
  2. RFID is short for “radio frequency identification”, which in this case allows a reader to identify the value and location of every poker chip at the table.

Tags:
Category:

Leave a Reply

Your email address will not be published. Required fields are marked *