What Should I Expect Before a Round of a Popular Drinking Game?

A Data Analysis of Riding The Bus

Recommended equipment for Ride The Bus

College. It’s a time for things like exploring your personality, finding your values, and making lifelong friends. Those are all well and good, but college is also a time for drinking games! There’s plenty of time in the day for more noble goals, but the night requires novel ways to drink beer or sip gin and tonics. There are plenty of entertaining drinking games, but Ride The Bus in particular raises some interesting data questions.

Drinking games usually incorporate giving others drinks as a reward, having to take drinks as a ‘punishment’, and then a whole lot of luck to make things fun. Ride The Bus incorporates all of these aspects into a three phase card game where the infamous third phase can test the resolve of even seasoned college students.

Some rounds you can get away with only one or two drinks. Other rounds it can feel like you are taking a drink every few seconds. So what exactly should someone expect to drink during a single game? Data analysis and millions of simulations have the answers.

Note: There are many different versions of this game, but I will explain the version I am using briefly before each section.

Phase 1: Getting Cards

How It Works:

A dealer asks each player four questions while giving them cards. If the player gets it right, they give a drink. If the player gets it wrong, they take a drink.

“Red or black?” Guess the color of your 1st card. “High or low?” Is your 2nd card going to be higher or lower than your first? “Inside or outside?” Is your 3rd card between or outside your first two? “What suit?” Guess the suit of your 4th card.

If a card is on the edge, then the drink stake is raised by one and another card is given. For example, if your first card is an 8, you say higher, and your second card is an eight, then you simply guess high or low again for a higher risk.

Players will end up with 4 or more cards.

Data:

On average, you will have to take 1.8 drinks, but get to give out 2.4 drinks during this round. This phase is a light introduction that promotes giving more than taking. Rather than just hand out cards, a little bit of fun is added.

Below is a heatmap of the amount of drinks one can expect to give or take during the first phase. Rarely will one get to give or take more than 3 drinks.

Phase 2: The Pyramid

How It Works:

The goal of this phase is to get rid of your cards. A pyramid of face-down cards is set-up with four rows. The bottom row has four cards while each higher row has one less.

The dealer will flip over cards starting at the bottom and working up. If you have a card that was flipped over, you can put that card down on the pyramid and give out a drink. If the card was on the first row give one drink, the second row, two drinks, and so on.

The player(s) with the most cards left in their hand have to “ride the bus” in the third phase.

Data:

In this phase, the drinking stakes go up. On average, one can expect to give out 3.9 drinks during this round. If everybody is giving out drinks randomly, one can expect to take that many drinks too, but there’s always the chance you get singled out to take much more than that.

Below is a histogram of the number of drinks you could give out during the pyramid phase. The meat of the distribution is around 0–7 drinks, but the possibility of giving out ten or more drinks is very real.

Giving out drinks during this round is fun, but the key aspect is finding out who has to ride the bus in the next round. The more players there are, the less likely one has to ride the bus. The below plot shows your probability of having to ride the bus based on how many players are in the game.

Yikes! Because of the chance of ties in the max number of cards, the odds of riding the bus are significantly more than 1/(number of players). Even with 10 people, you have a 1/5 chance of riding the bus. Especially in small groups, having to ride the bus is very likely.

Phase 3: Riding The Bus

How It Works:

Only the players selected to ride the bus in the second phase participate in this last phase. The dealer places seven face-down cards in a row. A dealer will flip over a card and ask the players, “High or low?” The dealer then reveals another card on top of the card in question.

If the players are right, they flip over the next card. If the players are wrong, they start from the beginning again. Players have to get seven guesses in a right to get off the bus and win the game.

The most daunting part of the game, riding the bus is a highly random event that can be stressful when losing, but exuberant once it ends.

Data:

Counter-intuitive to the reputation of this phase, on average, you can expect to only have to take 4.9 drinks before getting off the bus. Certainly not a low number, but sometimes it can feel like the average is 20 or 30 drinks based on how long it can sometimes take to get off the bus.

The below plot shows the probability of each amount of drinks taken while riding the bus.

The modal outcome is to get all seven cards in a row correct without taking any drinks! This graph almost exactly resembles a distribution called the exponential distribution. The important aspect of the exponential distribution is the “memoryless” property.

What that means is that no matter how many drinks you have already taken while riding the bus, you should always expect to have to take 4.9 more drinks before getting off. Even if you are already 100 drinks in (very unlikely), you should expect 4.9 more failures before getting off the bus. Keep this in mind the next time it feels like the bus is never going to stop!

The below plot is the same information as above, but shows the cumulative probability instead. For example, the probability of having to take 12 or more drinks is ~10%.

Yikes again! The downside risk of large numbers of drinks is large. Only until around 16 drinks is it unlikely to have to make it that far without winning.

Conclusion

In a six player game, assuming drinks are given out randomly, one can expect to have to take 9.5 drinks in total. Still, there is a large risk of having to take double or more of that depending on if you have to ride the bus and how long it takes.

I hope that I haven’t ruined the fun of the game with numbers! Stay thirsty my friends and keep riding the bus.

Code: https://github.com/DastonArman