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Playing Credit Card Roulette

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Credit Card RouletteLove 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. :)

How to Play Credit Card Roulette

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)

Expected Value

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.

Buying Out

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.

Insurance

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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17 Responses to “Playing Credit Card Roulette”

  1. tom says:

    I’ve played once for a $90 check. 1st card picked, pays.

    That first card was me…

  2. Ross says:

    Hi Jim,

    I have to disagree with your assessment a bit about Credit Card Roulette. While mathematically your expected value is correct, you’re assuming a constant state of variables (e.g. I go to lunch every Friday at the same restaurant with the same 4 coworkers, and we play credit card roulette). Under those circumstances, you are mathematically bound to end up even.

    But often times, there is no constant means of playing the game. Either the amount of people at the meal differs, or the cost of the meal varies, or you just don’t play frequently enough.

    The way I like to think about it is this: if a casino had a game where you could put down $200 (the tab) to win $20 (your meal), would you do it? No.

    While I’m a fan of the game from an entertainment perspective — it is very exciting when the card is pulled out — I do not believe it to be a smart risk, only a fun one.

    Fun article!
    Ross

    • Jim says:

      I don’t see how the other variables (how often, with whom you play isn’t important, etc.) affects it. The only real variable in the game is how much your food costs. If it costs less than the average, then you always lose (since your expected value is no longer zero). If your costs are greater than average, you always win. In actuality, the expected value is rarely zero but it has nothing to do with the other factors. It’s simply how much you’ve “spent” on the meal. I would take the $200 bet if the odds were correct. If I could win twenty bucks 99% of the time, then yes I’d do it.

      You are correct about coming out even though. The more games you play, the more the results will trend towards the expected value. However, the only way to make smart decisions is on a game by game basis and EV is the only way to do it.

  3. Geoff says:

    Jim- I play credit card roulette all the time and love it….it just makes dinner more fun and even when you lose you still get to treat your friends….and I find you usually get free drinks the rest of the night.

    I never heard of “buying out”, but love the idea! I’m definitely going to start incorporating that.

    Incidentally, I invented a similar game (and posted about it a few months ago). “credit score roulette”. Very similar, but instead you wager on who has the highest credit score out of your group (and the lowest has to pay for a night out).

  4. Hunter says:

    I can’t wait to give this a try. Seems fun and fair, as long as the waiter/waitress is neutral. It would be easy to tip the scales if you were that way inclined.

  5. Strebkr says:

    I’m glad to hear others play this game as well. I didn’t know it was this big. I first heard of it at training for my old company. We were just out of school with company credit cards at training. We would try to find awesome places to go out to dinner when out of town. It was all being reimbursed by the company, but it was still a bit of a rush to play. We played the last card picked has to pay. It keeps the suspense up longer. I highly recommend playing that way.

    As for buying out and insurance, you need to have likeminded people with you or else they might get too confused or think “the numbers” guys are too weird.

    Ha – Great post. I’m certainly forwarding this to everyone I used to play with.

  6. zapeta says:

    I’ve never played this but it sounds like fun. My friends and I are boring, we just pay our bills individually.

  7. Amy Saves says:

    Definitely not a game for the faint of heart or those on a budget. Although, I suppose if you are super lucky and on a budget, then you win out!

  8. Strebkr says:

    Amy, it really works out if you tend to go out with the same people many times and you all order about the same amount of stuff.

    Its probably not fair to the vegetarian who goes to the expensive steak joint and gets stuck paying for everyone’s $50 steaks.

  9. skylog says:

    haha, this is great! i have never heard of this but i think it would be great fun. my only problem is that i generally go out with such different groups of people that i do not think i would be able to get a stable group of people to do this with.

    either way, thanks for the idea!

  10. Jay says:

    What we usually is have the waiter/waitress shuffle the cards behind their back….they shuffle for alittle and then throw a card on the table….that person is the loser….me and my friends play all the time….great game.


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