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Playing Credit Card Roulette
Posted By Jim On 03/31/2011 @ 11:46 am In Personal Finance | 17 Comments
Love to gamble but don’t live close to a casino? Why not give credit card roulette a shot? Here’s a game that you can play anytime you go out, as long as you have a few other gamblers with you, and it’s probably high stakes enough for you to satisfy that craving without costing you too much money.
The last time I played this game was at Ra Sushi in Las Vegas  (great happy hour prices by the way, $1 saki is unbeatable). We had a party of at least fifteen people (we’re talking a bill that was easily north of $600, that’s with happy hour prices!) with almost everyone buying out, leaving only four of us left. One participant decided to buy in two spots (take the money and put in more cards) and give himself a 50% chance of paying the entire bill. I was sweating bullets as the waitress removed the cards, fortunately mine was the second one removed. Not all the gambling happens at the casino.
The next time you go out for a meal, or any situation in which a bill is shared, ask your friends if they’d like to give credit card roulette a shot. Assuming everyone purchased roughly the same dollar amount in food and drink, the game works out from a fairness perspective. First, everyone puts a credit card into the “pot.” Then, when the waiter or waitress comes over, he or she will start removing cards one by one. The last card remaining pays the entire bill.
(There are variations where the first card pulled pays for the meal, but it’s the same idea)
As any good gambler knows, it’s all about expected value, right? In this case, the expected value in credit card roulette is zero. You have neither receive nor give an edge or advantage with this bet. It’s like flipping a coin.
The Math: In a 5 person game and a $200 check, 20% of the time you are chosen and pay the $200, or $160 more than your actual share. 80% of the time you pay $0, or $40 less than your actual share. 20% of -$160 plus 80% of +$40 = $0.
Does it matter which variation of credit card roulette you play? No. Above, I explained two ways to play – “removing the cards one by one with the last card paying” and “the first card removed pays.” From a probability perspective, the two are identical because participants can’t do anything as cards are being removed (1/5 vs. 4/5*3/4*2/3*1/2=24/120=1/5). The first way is simply more suspenseful, especially if you have a large bill and a large number of participants.
If you have a large group, there are inevitably going to be diners who don’t want to play. That’s entirely fair. What we typically do is let them buy out of the game by paying their share of the bill. The person who “loses” will get the cash. For the true gamblers in the group, they may “buy” that person’s spot in the game by putting in an additional card and taking the cash. Remember, the expected value of their bet is still zero since the pot has grown in lock step with the probabilities.
Here’s a fun, albeit somewhat complicated, wrinkle that is only possible in the case where the waiter/waitress pulls out one card at a time (with the last card paying). If you’re quick with calculated expected value, you can calculate the odds someone will lose and offer them insurance. The idea is that the person offering insurance is making a positive expected value bet and the person buying it is getting out of the game.
Let’s say you have five people in for a $100 check, or $20 each. After the first card is removed, the remaining four people have a 25% chance of paying the $100. Their expected bill has just increased from $20 (20% of $100) to $25 (25% of $100). I can offer insurance to one of those participants and it makes financial sense for me if they pay more than their expected bill (I essentially take their place in the game).
Let’s say I offer insurance for $30 (they’re really paying just $10 for the insurance, since they owed $20 at the start of the game) and someone takes me up on the offer. I have a 25% chance of paying $100, or $70 after the insurance payment of $30, and a 75% of paying $0, or earning $30. My expected value is $5 (0.75 x -$70 + 0.25 x $30), so I’ve made a positive “bet.” They get to avoid the possibility of being on the hook for the entire check!
I’m sure there are a lot of variations and add-ons to this wonderfully vicious game but those are just the ones I’m aware of or have experienced. The fun of the game is the expense and in the cheering that occurs when you see your own card get removed from contention.
(Photo: netinho )
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 Ra Sushi in Las Vegas: http://www.rasushi.com/
 netinho: http://www.flickr.com/photos/johnwardell/80125882/sizes/l/
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