Measuring Human Adaptation to AI in Decision Making:
Application to Evaluate Changes after AlphaGo

In our first study, we examine the Human-AI Gap to compare human players’ strategies before and after the launch of AI programs. The measure allows us to evaluate how close each move decision of human players is to the level of AI programs, and thus to determine if human decisions improved after AI programs were available. When AI programs did not exist, human players gained new information on Go game strategies by going over top players’ move decisions in tournaments, and discussing the strategies with other human players (illustrated in Panel (a)³³3“The power of Korean Go? Joint research!” Mar/09/2011 (https://www.donga.com/news/Culture/article/all/20110309/35417308/1) in Figure 1). What made AlphaGo so sensational in the human Go community is that the AI program used many unorthodox tactics. AlphaGo’s demonstration of unfamiliar but effective strategies motivated human players to discuss and learn the strategies of AI. Consequently, the way human players study winning strategies completely changed into getting tutored by AI (illustrated in Panel (b)⁴⁴4“Hone your Go skills with AI instructors” Feb/26/2019 (http://www.munhwa.com/news/view.html?no=2019022601032103009001) in Figure 1).

Interestingly, two different AI programs were released at different times. One is AlphaGo in March 2016 and the other is open-source AI programs (e.g., Leela Zero) in October 2017. The main difference between the programs is whether players can observe the programs’ intermediate reasoning process behind each move decision. AlphaGo and its subsequent versions show its actions only (i.e., a sequence of positions where AI placed stones). However, the open-source programs and education tools provide information on the detailed thought process behind each AI action. They show the contingency plan of AI such as how AI would respond to a hypothetical state following each counterfactual choice at any states. This allows human players to review the strategies of AI under various states. Also, humans observe how AI evaluates each state of a game (e.g., the current win probability⁵⁵5Although we use the term win probability, its exact interpretation is more subtle. Still it is used in the Go community so we follow this term. of each player and change in win probability if the human player chooses to deviate from AI’s best move). More details on what information is given to human players are explained in the Appendix. We leverage the fact that two AI programs giving two different learning materials to human players were released sequentially. It gives us a chance to examine the conditions under which human players adapt to AI.

Our data spans from January 2014 to March 2020 and it comes from official matches between human professional players. It consists of two datasets: (i) 30,995 matches between 357 Korean professional players, where we observe match date, the identity of players, and match outcomes, (ii) 1.3 million move decisions of the Korean professional players from matches between human players. We webscraped the datasets from the Korean Go Association and other websites⁶⁶6Not every match has been saved with a detailed record of move decisions, but we collected the historical data from multiple sources to get more complete history. The data containing match results spans from 2012 to 2020. The data containing move decisions spans from 2014 to 2020.. For every single move choice by a human player, we simulate the optimal move decision of AI⁷⁷7We use an AI program called Leela Zero to analyze our data. We use GPU provided by Google Colab Pro (P100) in our simulation. under the same state of the game and compute our measure by comparing a value network of human players’ actual choice and that of AI’s choice. Thus, we have 1.3 million move decisions of human players, 1.3 million move decisions of AI, and AI’s evaluation of each of these decisions. The gap between a value network of human decisions and that of AI decisions is our measure of the human decision’s effectiveness.

Table 1 shows the summary statistics of the data. Our data includes heterogeneous players in terms of performance, whose winning rate is 43% on average. For each match, two professional players make an average of 216 move decisions. AI evaluation on each move decision indicates that human players make sub-optimal choices, which results in a 3.5% loss in win probability.

We calculate the Human-AI Gap ($\Delta$) for every decision made by every human player in our dataset. A value of zero means that a human player completely replicated the AI’s decision ($\Delta_{k}=0\iff a_{k}^{Human}=a_{k}^{AI}$) and made the optimal move, while a positive value indicates the extent to which AI’s decision was superior to that of the human player, or put differently, the extent to which the human player’s decision quality trailed that of the AI. We present the pattern of $\Delta_{k}$ in Figure 2. The average Human-AI Gap of each set of 10 moves (e.g., $1^{st}-10^{th}$, $11^{th}-20^{th}$, …) is plotted across the course of match. The solid red curve traces the Human-AI Gap before AlphaGo beat Lee Sedol (from January 2014 to March 2016); the dotted green curve traces the Human-AI Gap between AlphaGo’s debut and the release of open-source AI programs (from March 2016 to October 2017); lastly, the dashed blue curve traces the Human-AI Gap after open-source AI programs were publicly released (from October 2017 to March 2020).

Perhaps the first thing that jumps out in Figure 2 is the inverted U pattern of the Human-AI Gap across moves. We speculate that the pattern emerges from two opposing forces at work. First, as the match progresses (and the move number increases), finding the optimal moves becomes harder because stones interact with one another more. For example, in the beginning, when there are only one, two, or several stones, the black and white stones tend not to interact much with each other, as both players seek to control open territory in the corners and sides that are free from either side’s influence. In this early stage, human decisions are not too inferior to AI’s decisions, leading to a smaller Human-AI Gap for earlier moves. As the game progresses (post opening stage), however, black and white stones now clash against each other to fight for territory. In this early to middle stage of the match, optimal moves require thinking not only about how to control more territory as in the beginning, but also how to capture the opponent’s stones or how to survive under the opponent’s attack. Thus, this clash in the early to middle stage of the match presents a greater challenge for the human decision maker, and as a result, human decisions are inferior to AI’s decisions by a greater margin, leading to a greater Human-AI Gap for moves in the middle stage. The Human-AI Gap peaks at a point and starts decreasing, however, because of the second, opposing force: the more stones there are on the board, the fewer possible moves become available. For example, in the middle stage, there may be 30 possible moves to consider, whereas by the end of the match, there may be only 5 possible moves to consider. With fewer possible moves to consider, the human player can find the optimal moves more frequently, and as a result, human decision quality more closely approaches AI decision quality. We speculate that these two opposing forces give rise to the inverted U shape of the Human-AI Gap.

Using our measure of the Human-AI Gap, we are able to observe the pattern of human decision quality over the course of a match. One possible insight from this observation may be that room for improvement is greatest in the middle stage of the match, because the middle is where the Human-AI Gap is the greatest. Human players may find that studying moves in the middle stage may improve their game more than studying moves in the early or late stage of the match. Thus, our measure of the Human-AI Gap can be used to coach human players on what to study. Another possible insight may be that trying to improve human decision making in the middle stage of the match is futile. Human experts may have concluded that improving their middle-stage game is very difficult as compared with improving the early-stage game. That is, although human experts have managed to improve their early-stage game (the red, solid line shifting down to the blue, dashed line for Moves 1-50 in Figure 2), perhaps they could not improve their middle-stage game despite much effort (the blue, dashed line overlaps the red, solid line for Moves 51-140 in Figure 2). Improving the middle-stage game may be very hard, perhaps due to intractable complexity and lack of similarity from one match to another, both of which may prevent discovery or learning of any new principles. If so, human experts may instead double down and focus their effort even more on improving their early- or late-stage game. Whichever insight may reflect reality, our measure could be useful in suggesting how human experts’ effort should be allocated.

More important than the inverted U pattern are downward shifts in the Human-AI Gap (for Moves 1-50). Interestingly, the Human-AI Gap decreased only a little bit after human players could observe AlphaGo’s actions, as evidenced by a barely noticeable downward shift from the “Before AI” curve to “After AlphaGo” curve in Figure 2. In contrast, the Human-AI Gap dropped markedly after open-source AI programs became available, as evidenced by a larger downward shift from “After AlphaGo” curve to “After open-source AI” curve in Figure 2. Here we do not take into account a difference between players. So we construct a data set at the player-month level ($\Delta_{it}$) in the following way.

where $\Delta_{it}$ denotes player $i$’s average gap in month $t$. $n_{it}$ stands for the number of matches a player $i$ has in month t, and $k$ represents the order of a choice within a match $j$. Using a panel structure, we can investigate whether human decision quality indeed increased more after open-source AI became available than after AlphaGo’s debut. Because the decrease in the Human-AI Gap was concentrated in the early and middle stages of the game (Moves 1-50), and because no such decrease was readily observable for Moves 51-140, we focus our attention on the first 50 moves in each match when we investigate human decision quality over time next (so $K=50$).

We examine the Human-AI Gap over time after controlling for individual difference. As defined earlier, $\Delta_{it}$ denotes player $i$’s average gap in month $t$. Then we run the following regression: $\Delta_{it}=\alpha_{i}+\tau_{t}+\epsilon_{it}$, where $\alpha_{i}$ is a player fixed effect, $\tau_{t}$ is a time fixed effect, and $\epsilon_{it}$ is an error term. In Figure 3, we report the estimated time trend, $\hat{\tau_{t}}$. The red vertical line on the left marks March 15, 2016, the date of the match between Lee Sedol and AlphaGo, and the red vertical on the right marks October 25, 2017, the date when the open-source AI program Leela Zero was publicly released, which was followed by releases of similar AI programs and education tools. Consistent with a tiny downward shift in Figure 2, we see little change in the Human-AI Gap in the period between the two red vertical lines. The Human-AI Gap significantly drops after the second vertical line indicating the time when open-source AI and its analysis tools became available. The decline in the gap over time shows that human players adapted to AI programs gradually, more so after the educational tools were available. The finding provides suggestive evidence that human players modified their choices and did better in Go matches after gaining access to AI.

In our second study, we examine how our measure can be useful in detecting one negative form of adaptation to AI: receiving help from AI to gain an unfair competitive advantage, i.e., cheating. In September 2020, a 13-year-old professional Go player cheated in a match against a 33-year-old top-notch Go player by using an AI program that suggests optimal moves for given states. The high-stakes match (one of Round of 32 matches in a tournament that awards $175,000 in total prize money) was held online due to a COVID-19 lockdown, opening door to the possibility of cheating, which would have been difficult to pull off had the match been held offline with many eyes around. Not surprisingly, the cheating player showed an extraordinary performance in the match, and as a result, a debate ensued on online forums regarding whether she received help from AI. The controversy culminated in the cheating player finally confessing her transgression in November 2020. Would our measure be sensitive enough to detect such cheating behaviors?

We first obtain move data for all 52 matches of the cheating player’s professional career, including the match in which she cheated. We then use an AI program to calculate a winning probability associated with each move in these 52 matches and a winning probability associated with an AI’s optimal move. As in the first study, we subtract the former from the latter to calculate the Human-AI Gap. To be consistent with the previous study, we focus our analysis on the first 50 moves by each player in each match. This results in 50 values of the Human-AI Gap for the cheating player in the cheating match and 2,375 values in the 51 non-cheating matches (after missing values were removed), for a total of 2,425 values in all 52 matches.

We hypothesize that our measure of the Human-AI Gap could detect an increase in the cheating player’s decision quality when she received assistance from AI as compared with when she did not. Indeed, that is what we find. In the cheating match, the cheating player’s move decisions show smaller Human-AI Gaps (M = 1.02, SD = 2.13), indicating better decision quality, than move decisions in the non-cheating matches (M = 2.35, SD = 4.30), t(57.78) = 4.23, one-tailed p $<$ .001, Cohen’s d = 0.31 (see Figure 4). Two nonparametric tests show converging results. A Wilcoxon rank-sum test reveals that Human-AI Gaps are more likely to be smaller when she cheated (Mdn = 0.60) than when she did not cheat (Mdn = 0.75), W = 67883, one-tailed p = .041. Similarly, a two-sample Kolmogorov-Smirnov test reveals that the Human-AI Gaps in the cheating match and those in the non-cheating matches have different distributions, D = 0.23, one-tailed p = .006. Results from these three tests show that our measure of the Human-AI Gap can be useful to detect higher decision quality from cheating. But can our measure also detect greater stability in decision quality from cheating? We hypothesize that the Human-AI Gap will be more stable across the moves in the cheating match than in the non-cheating matches, because moves suggested by AI will be consistently optimal, whereas moves made by the human player herself will be optimal less consistently (less frequently). In other words, we want to test whether our measure will exhibit lower variance (more stability in decision quality) in the cheating than in the non-cheating matches. As expected, a Levene’s test reveals that variance in decision quality (i.e., the Human-AI Gap) is significantly lower in the cheating match (var = 4.53, SD = 2.13) than in the non-cheating match (var = 18.51, SD = 4.30), F(1, 2423) = 4.85, one-tailed p = .014. This study shows that our measure could be useful in detecting a negative form of adaptation to AI, namely receiving AI assistance for an unfair competitive advantage in a professional competition.

In addition to demonstrating the measure’s usefulness, this study validates our measure. We know some truth about the world—that cheating occurred—based on the cheating player’s public admission of wrongdoing, and our measure is consistent with this truth. In other words, if the Human-AI Gap indeed measures adaptation to AI, including cheating, we expect the mean Human-AI Gap to be lower in a cheating match than in non-cheating matches, which is exactly what we find. In Section 3 of the Appendix, we similarly validate our measure with data from the first study. Specifically, if the Human-AI Gap measures the extent to which human players have learned to play like superhuman AI, then players who won their matches may have played better and more like superhuman AI than players who lost their matches, all else equal. Again, as expected, moves by winning players show smaller Human-AI Gaps on average than moves by losing players, which validates our measure.

In March 2016, AlphaGo showed its superhuman performance by beating a world-class human champion. AlpahGo’s performance improved even more between 2016 and 2017 and the AI program beat human Go champions in all 64 online Go matches. In May 2017, DeepMind released AlphaGo’s moves in 50 matches between AlphaGo and AlphaGo. Then DeepMind made AlphaGo retired. Even though its impact was sensational, the released information to the public was limited to the AI’s final actions only. As summarized in the top plot of Table 4, human players could have access to AlphaGo’s final actions only (i.e., a sequence of positions an AI placed a stone). Because those actions are unconventional, it was not easy for human players to appreciate how AlphaGo would reach its actions. Human players often had heated debates to figure out the rationale behind the decisions of AlphaGo. Although AlphaGo provided new perspectives on the game strategy to human players, it was not the most ideal learning material because it did not provide that rationale to human players.

In late 2017, one-and-a-half year after AlphaGo, open-source AI programs such as Leela Zero were released. Unlike AlphaGo of which Deepmind did not publish the source code, the open-source programs enabled developers to devise education tools such as Lizzie. Using the education tool, human players could review their choices in the matches with other human players. They could compare their own evaluation on particular states with the one calculated by AI. By doing so, they could realize whether they were too optimistic or too pessimistic at certain points in the match. In addition, they could observe what AI would have chosen at the state of the match, where they ended up making a sub-optimal move.

As summarized in the bottom panel of Table 4, education tools provided information not only on the actions by AI, but also on the detailed thought process behind each action of AI. First, human players observe a set of actions AI considers promising as well as the AI’s final choice (colored circles in Part 1). The tool also shows how AI would respond to a hypothetical state following each counterfactual choice at the current state (Part 2). Basically, the tool allows human players to review AI’s strategy. Here, a strategy refers to a contingency plan of actions under various states.

Second, human players observe how AI evaluates each state of a game. The number inside colored circles indicates the expected win probability of each action¹¹¹¹11It is the output of a Q-function in computer science or a choice-specific value function in economics with the current state and each action as input. Strictly speaking, the technical definition is slightly different from the working definition of win probability but still, it measures the effectiveness of each action. (Part 1). Furthermore, the program shows the current win probability of each player (Part 3) and a change in win probability if a human player chooses to deviate from AI’s best move (Part 4). For example, human players can try departing from AI’s candidate actions (in colored circles), and get feedback on their own choice to quantify any loss the deviation generates. If they disagree with AI choice or evaluation, they can test their strategy and see how AI penalizes it.

Due to this feature of AI education tools, human players can review their choices in a match with other human players. Altogether, information on AI’s strategy and evaluation provided by education tools gives humans an opportunity to understand better AI programs’ underlying primitives behind each move decision.

Our main strategy to find more convincing evidence is to distinguish human professional players who did and did not have access to AlphaGo or to the subsequent AI programs. We take advantage of the mandatory military service in South Korea. South Korean male citizens are required to serve in the military for 18-24 months before age 29, which forces the military-serving players not to be able to participate in Go matches more than once a month and to be away from recent trends in AI programs related to Go. Specifically, most of them are expected to be confined in their military base but they get short-term leave every other month. We confirm from the data that players serving in the military can participate in a tournament once a month at most. They do not have enough time nor a high-performance computer to self-teach unfamiliar tactics, strategies, or insights discovered by AI programs. We have an official record of Korean players’ military service history. Thus, a treatment group consists of players who were not serving in the military when AI programs became available, and a control group is players who were serving in the military and did not have access to AI at least for 6 months.

Figure 5 represents a time trend of $\Delta_{it}$ of players in a control group. In figure 5, the y-axis is the Human-AI Gap ($\Delta$), the x-axis is time, and the two vertical lines represent when the AI programs were available. It shows no significant change over time in our gap measure of control group. It is a sharp contrast to the figure 3, which implies that the access to AI programs that make human players choose better move choices. We verify the finding by Difference-in-Difference estimation. Consider the following regression equation:

We report the result of $\hat{\beta}$ in table 2. The dependent variable is the average gap of each player in each month. Each column in the table is based on the different definitions of post-AI periods: all months after Event 1 (March 2016), months between Event 1 and Event 2 (Dec 2017), or months after Event 2 only. The treatment effect of access to AI, captured by the interaction term of (Treatment group) and (Post AI period), is only significant after Event 2. Human players could place their stones in better positions only after they could observe AI programs’ strategy (e.g., candidate moves at each state, simulated sequence of actions after the choice) and evaluation (e.g., win probability at each state, change in win probability depending on each candidate move) and understand AI’s underlying principles behind each decision. The effect is not significant after they observed AI programs’ actions at each state, which might have been considered a “black-box” that generates incomprehensible outputs.

To address a concern that serving in the military itself could have affected the Human-AI Gap, we study human players who served in the military before AI programs appeared, and implement the same statistical test as before. Specifically, we compare the Human-AI Gap between two groups: players that had to serve in the military in 2015 and those that didn’t. Then we limit the sample period before March 2016 when AlphaGo came out. We report the coefficient of the interaction term as table 2. Table 3 shows that the military serving by itself does not significantly affect the Human-AI Gap. Although human players’ match performance could have deteriorated, their move decisions were as good as those prior to military-serving according to the Human-AI Gap. Thus, we exclude the explanations that the result in 2 is driven by military-serving, and conclude that access to AI drives the effect.

Does the Human-AI Gap tend to be smaller for moves by winning players than for moves by losing players? Answering this question can be one way to test validity of our measure. Our measure would tend to be smaller for moves by winning players who presumably would have played more like superhuman AI than losing players would have. We thus compared the Human-AI Gaps of early- to middle-game moves¹²¹²12We exclude the moves in the very end-game (i.e., Move number $k$ is greater than 150), because the current version of our program uses the Chinese rule for compensating for Black’s initial advantage, which creates inaccuracies for calculating the Human-AI Gaps for end-game moves within matches under non-Chinese rules. Our data is constructed in matches with non-Chinese rules. by winning players (n = 494,509) to those by losing players (n = 494,857) across all matches. The average Human-AI Gap was indeed lower—indicating higher decision quality—for moves by winning players (M = 3.43, SD = 5.15) than for moves by losing players (M = 3.88, SD = 5.56), t(983655) = 41.9, p < .001, d = 0.084. A nonparametric, Wilcoxon rank-sum test also showed that the Human-AI Gaps were smaller for moves by winning players (Mdn = 1.66) than for moves by losing players (Mdn = 1.92), W = 129616117936, one-tailed p < .001. This indicates that even though the quality of each move is measured from the prediction of self-trained AI, it is also highly correlated with the outcome from matches between human players.