I played the card game Twenty-one for this critical play. It is an old game that traces back to 18th century France but later became popular in other Western countries and has different regional variants. It has both analog and digital versions and requires 2+ players to play. I played Twenty-one with another friend using cards with him being the banker (dealer) and me being the punter. We betted on questions instead of money (whoever wins can ask the other person however many questions the punter betted on) and added in the “split” mechanism where the punter can choose to split the two cards they received and bet twice on each card.
I argue that Twenty-one puts players at risk for addiction by striking a nice balance between luck and skill. It gives players a sense of autonomy through a series of choices like choosing whether to hit or stay, whether to split, and what Ace represents, even though the starting hands and draws are up to chance. Despite the randomness involved, the knowledge of the banker’s card and the remaining cards in the deck motivates players to make use of probability calculations to inform their choices. Compared with other chance-based games, Twenty-one draws players in with its simple rules and keeps them playing with either the expectation of getting good hands and draws in the next round or confidence in their strategies or both, which makes the game addictive to play.
In Anthony’s luck vs. skill system, Twenty-one falls into the high luck & high skill quadrant. It is high luck in that the player cannot control what hands they get, the next card in the deck, and the dealer’s unrevealed card. When lucky they can get a hand of 21 (with one kind being J or Q or K and the other being A) right off the bat; when unlucky they can draw a card that puts the sum of cards at 22. However, Twenty-one balances this randomness with room for strategies and skills. Since the player knows what cards they want to draw and what cards are left in the pile, they can technically figure out the likelihood that they will get a card that’s in their favor. For example, I currently have a sum of 13 and need a card of 8 or below to not lose (i.e., stay below 21). Then there is roughly a probability of 8/13 that I’ll get the card I want. A more hardcore player would also take into consideration the cards that have already appeared and the revealed card of the dealer when computing probabilities. This of course would require more complex calculations, putting a high demand on the player’s math skills.
Fig.1: An example of when the dealer got lucky with a hand that sums up to 21.
Initially I tried playing the game by calculating probability in my head but soon relied purely on intuition, which I believe reflects how most casual players play this game. There are three places in the game where I need to draw upon my intuition to make choices:
First, when deciding whether to hit or stay, I tend to hit unless the sum is 18 or above. This is not necessarily a reasonable choice considering that I have a close-to-half chance of going above 21 if I already have a sum between 13 and 17. But playing under the impression that the sum is not close enough to 21 to beat the dealer and there is a considerable chance to get a desired number, I chose to hit. When I won, I was aware of the component of luck, but also attributed the outcome to my risk-taking approach. And when I lost, I tended to attribute it to bad luck, which led to more rounds of playing with the hope of getting luckier next time.
The second point of decision-making comes when the player gets an Ace and needs to decide whether to use it as a 1 or an 11. If I don’t get a sum of 20 or 21 with an 11, I would use it as a 1. This revealed the psychology of hoping there are better cards coming up and a better chance of winning, an instance of how randomness leads to expectation that is not necessarily rational.
The third point of decision-making comes when the player decides whether to split the hands and bet on each suite. I tended to split, considering that it would give me a higher chance of winning at least one suite. This tendency is partially caused by our substituting money with questions, since it doesn’t hurt if I lose but it would be great if I win, so more rounds is better. But if played with money, this is actually a balanced choice, because it increases the chance of winning and the risk of losing simultaneously.
Through these three choice points, Twenty-one gives players the motivation to play by feeding their sense of autonomy and competence, creating the impression that their winning is not just all up to chance, but also owes to their personal character and good intuitions.
Fig.2: I used split and had 21 for both suites.
Similar to other chance-based games, another major factor that makes Twenty-one addictive is the experience of getting insanely good cards and the prospect thereof. In one round, I used “split” and ended up getting 21 for both suites. Once this happens, such ideal situations with extremely low probability would greatly satisfy the player’s need of achievement and acquisition (if playing with money) and keep the player playing in order to experience that adrenaline rush again.
But what distinguishes Twenty-one from other chance-based games is the simplicity of its rules and the sole focus on winning the challenge. As a newbie to card games, I was able to have a good grasp of the game quickly due to its straightforward rule of reaching 21 or getting close enough to it. Although the game mechanics are not as intricate as Texas Hold’em and Three Card Poker, I actually found this game to be more fun because I don’t have to constantly think about the dominance order or making strategic use of cooperative play. Each round of the game was also pretty quick so it also lured me in again and again to try out my luck and validate my intuition.
