The outcomes are only important insofar as they affect your next EV calculation. You can make great strides in decision-making simply by analyzing past choices in terms of their EV and not the results. In that case, you’d see that in your dinner with Gary, you’ll end up paying as much as him-and everyone else-on average: very close to $200. ![]() This basically functions as a mathematical representation of excitement the reason it would feel like such a relief to not pay after having your card in the final two, for example, is that your EV immediately drops from -$1,000 (-$2,000 * 0.50) to $0, since once you’re eliminated your new chances of paying are 0%.Ī useful tool for thinking about probability is to basically ignore what happened in reality and instead ask yourself what the outcome would be if you could play out the same scenario with the same variables a million times. The EV does change as the game progresses, though, assuming you eliminate one card at a time. You both paid in EV, and it just so happens Gary was unfortunate enough to see his 10% chance of paying $2,000 actually realized-but that doesn’t change the EV. The fact that you have the benefit of hindsight to see your range of outcomes shrink from a 10% chance of paying to 0% is irrelevant unless someone is cheating in the game to increase their EV, you should think about the difference between what you paid and what Gary paid as $0, because that is what the difference in EV was when you made the decision to play. That might seem ridiculous, but it’s really how you have to think to be a sound probabilistic decision-maker. Gary owes you a thanks just as much as you owe him one you both paid the same amount. Your EV was -$200, just like everyone else’s, as you risked a 10% probability of getting stuck with the same check. ![]() Yes, it sucks for Gary, but in reality, you took on just as much risk as he did. While Gary paid $2,000, no one knew who was going to pay before playing the game. Thinking about the world in terms of probabilities and EV means not retroactively looking back on decisions as “good” or “bad” or recalculating the math based on one outcome. Why? Because you paid just as much as he did. Not only do you not need to pay a dime for your meal, but you also don’t need to say thanks to Gary. Now here’s why CCR is so fun when you win. The 10 of you live it up with a $2,000 bill and your friend Gary loses CCR and is stuck paying. Let’s say you go out to a fancy meal with nine friends. I bring up CCR because I think it’s an easy example of how to properly think in terms of probabilities and EV (expected value). The only asymmetry in CCR is if someone continually orders more than you. Of course, that is expected to even out over the long run. ![]() I’d estimate I’ve played 100 times and paid maybe 50% of what I “should have” based on my meals. But, of course, 1-in-10 times you’re paying for everyone to eat. In a group of 10, you’re eating for free 90% of the time. If you’re eating with more than one person, most of the time, you’re going to get a free meal. It’s actually quite a fun sweat on bigger bills, so I highly recommend playing if you can withstand the swings.ĬCR turns a 100% chance of a small meal payment into a smaller probability of a larger payment. If it’s a bigger bill with a little more on the line, we might ask the server to get involved, usually selecting one at a time to not pay until just a single card remains. If it’s just a few people, we just mix up the cards, hidden away from view between someone’s hands, then have someone pick a random one to pay (“top card pays,” for example). If you’re unfamiliar, “CCR” is a game in which everyone puts in a credit card to be selected at random to pay the entire check. Whenever I eat out with my gambling buddies, we play a game called “credit card roulette” to settle the bill.
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