All subjects were naïve, had normal or corrected-to-normal vision, and were paid $15 for a single experimental session (∼60 min). Experiments were carried out under the guidelines of the Barrow Neurological Institute’s Institutional Review Board (protocol 04BN039) and written informed consent was obtained from each participant. Nine subjects (3 females, 6 males) participated in Experiment 1. Six new subjects (2 females, 4 males) participated in Experiment 2. Eight new subjects (1 female, 7 males) participated in Experiment 3.

Subjects rested their head on a chin/forehead-rest 57 cm from a video monitor (Barco Reference Calibrator V, 60-Hz refresh rate).

Eye position was acquired non-invasively with a fast video-based eye movement monitor (EyeLink 1000, SR Research) at 500 samples per second (instrument noise 0.01° rms). We identified and removed blink periods as the portions of the EyeLink 1000 recorded data where the pupil information was missing. We added 200 ms before and after each EyeLink 1000 identified blink period to further eliminate the initial and final parts of the blink, where the pupil is only partially occluded. Eye positions during the blinks were calculated by linear interpolation from the eye positions at the beginning of the blink to the end of the blink (Bour et al., 2000).

All videos had the same frame size [26.7° (w) × 14.1° (h)] and were displayed centrally on the monitor screen [40° (w) × 30° (h)]. Video clips S1–S5 in Supplementary Material may be divided into four segments: (1) “Before Toss” refers to the performance from the start of the video to the initiation of “Toss.” During this period, the magician either throws a coin up in the air, using his right hand (as in Videos S1–S3, S6, and S7 in Supplementary Material) or pretends to do so (Videos S4 and S5 in Supplementary Material); (2) “During Toss” is the period from toss initiation to the end of the toss (i.e. beginning of “After Toss”). The “Toss” can be either a “Real Toss,” i.e., the magician throws a coin from right to left hand (Videos S2 and S7 in Supplementary Material) or a “Fake Toss,” i.e., the magician either pretends to throw the coin from right to left hand, but surreptitiously retains it in his right hand (Videos S1, S3, and S6 in Supplementary Material), or simply performs a tossing gesture (i.e., without a coin) from right to left hand (Videos S4 and S5 in Supplementary Material); (3) “After Toss” extends from the end of toss to the opening of the magician’s left hand; and (4) “Reveal” from the opening of the left hand to the end of the video. That is, the “Reveal” stage starts at the time the magician first opens his left hand, and ends with the last frame of the performance.

Videos S6 and S7 in Supplementary Material are identical to Videos S1 and S2 in Supplementary Material, respectively, except that the “Reveal” segments are omitted.

Subjects pressed a key to start each trial. A blank screen lasting for 2 s was followed by a short video clip of Mac King performing one of two maneuvers: Magic Trick or Real Toss. Both videos stopped before the magician revealed the inside of his left hand (Figure 1A; Videos S6 and S7 in Supplementary Material). Subjects were asked to press a button, as soon as possible, in the event that they saw a coin flying from the magician’s right hand to his left hand.

Each condition (Magic Trick or Real Toss) was presented for 50 trials, amounting to 100 trials in a single session. Trials were pseudo-randomly interleaved.

When Mac King actually tossed the coin from right to left hand (Real Toss), subjects indicated that they saw the coin toss 93.5% of the time, throughout the 50 trials presented (Figure 1B). When Mac King only pretended to toss the coin (Magic Trick), subjects reported at first a coin toss 72.6% of the time (averaged across the first 10 trials). This initial percentage dropped to 52.4% for the rest of the trials, reflecting the effects of the subjects’ learning to discriminate between real and illusory coin tosses (the subjects performance in the first 10 trials was significantly different from that in the remaining 40 trials; two-sample t-test, p < 0.01). Thus, subjects were able to distinguish between the two experimental conditions with maximal sensitivity after about 10 trials of each condition (that is, 20 trials combined). Figure 1C illustrates on a trial-by-trial basis the percentage of times that a coin toss was reported. Despite significant variance in the subjects’ responses across time, the percentage of coin toss reports decreased steadily for the first few trials, stabilizing at around trial number 10.

Experiment 2 followed the design of Experiment 1, except that both video clips (Magic Trick and Real Toss) now included an additional “Reveal” stage, where the magician opened his left hand to reveal that it was empty (Figure 2A; Videos S1 and S2 in Supplementary Material).

When Mac King actually tossed the coin from right to left hand (Real Toss with Reveal), subjects indicated that they saw the coin toss as often as in the equivalent condition (Real Toss without Reveal) from Experiment 1 (91.3% of the time, throughout the 50 trials presented; Figure 2B). When Mac King only pretended to toss the coin (Magic Trick with Reveal), subjects reported at first a coin toss around 62.9% of the time (averaged across the first 10 trials). This initial percentage was not significantly different from that obtained in the equivalent condition (Magic Trick without Reveal) from Experiment 1 (paired t-test, p > 0.05). The next 40 trials represented a distinct departure from the results from Experiment 1, however, as the coin toss reports dropped to 21.9% (a significant difference from the matching data in Experiment 1; paired t-test, p < 0.001). Thus including a “Reveal” stage with each performance allowed the subjects to gain additional information after about 10 trials of each condition (that is, 20 trials combined), thereby improving their discrimination of a real coin toss versus a simulated maneuver. Figure 2C illustrates on a trial-by-trial basis the percentage of times that a coin toss was reported in Experiment 2.

Detection sensitivity and response bias were comparable in Experiment 1 (No Reveal) and Experiment 2 (Reveal) when we considered all 50 trials together, suggesting no effect of the “Reveal” stage (Figure 3, Left Column; see Materials and Methods: General for details on signal detection analyses). However, when we separated the first 10 trials from the last 40 trials, we found that the presence of a “Reveal” stage led to a significant increase in detection sensitivity (d′) in the last 40 trials (Figure 3, Right Column). This result suggests that the information obtained from the “Reveal” stage helped subjects to discriminate between real and simulated tosses, after a number of trials.

Experiment 3 followed the design of Experiment 2, except that we presented 5 different video clips: Magic Trick, Real Toss, Two Coins Fake Toss, Final Coin Fake Toss, and No Coin Fake Toss (Figure 4A; Videos S3–S5 in Supplementary Material). The Magic Trick and Real Toss video clips were identical to those in Experiment 2. The three additional video clips portrayed the following maneuvers: In the Two Coins Fake Toss, Mac King pretended to toss a coin from right to left hand, but actually retained it in his right hand. Subsequently, he opened his left hand to reveal a second coin that had remained hidden (in the left hand) until the reveal. In the Final Coin Fake Toss, Mac King pretended to toss a non-existent coin from right to left hand, and subsequently opened his left hand to reveal an actual coin (which had remained hidden in his left hand until that point). In the No Coin Fake Toss, Mac King pretended to toss a non-existent coin from right to left hand, and subsequently opened his left hand to reveal that it was empty.

Two main motivations of this experiment were to determine the potential effects of (a) the magician’s use of social misdirection cues and (b) the observer’s gaze position on the perception of this magic trick. Thus, each of the videos was presented with (a) the magician’s face visible and occluded, and (b) two different viewing conditions: free-viewing and fixation (Figure 4B), for a total of 20 conditions (5 types of video clip × 2 face conditions × 2 viewing conditions). We presented 5 trials for each condition, amounting to 100 trials, pseudo-randomly ordered, in a single session.

In the Face Occluded condition, the face of the magician and surrounding area was blocked by an 11.9° (w) × 5.6° (h) black rectangle. In the Face Visible condition, no occlusion was used.

In the Fixation condition, subjects had to fixate a small red cross (0.75° wide) within a 2° × 2° fixation window, placed in the midpoint between the magician’s eyes (in the first frame the magician oriented his gaze to the viewer), or on the corresponding location in space when the magician’s face was occluded. This fixation window was invisible to the subjects. A trial was discarded whenever the subject’s gaze left the fixation window for more than 500 ms (<500 ms gaze excursions were permitted to allow for blinks). Then the discarded trial was inserted randomly into the subsequent queue of trials and presented to the subject again.

In the Free-viewing condition, no fixation cross was presented and subjects were free to explore the visual scene at will. Before each trial, we presented an instructions screen indicating whether fixation or free-viewing would be required.

The strength of the illusion was remarkable: subjects perceived illusory coin tosses a large fraction of the time, including during those trials in which the magician never showed a coin in the initial hand (Final Coin Fake Toss and No Coin Fake Toss conditions; Figure 5).

Joint attention is the mechanism by which an observer can share the experience of another by following his/her gaze direction and pointing gestures. Magicians rely on joint attention as a form of social misdirection, to direct the spectators’ attention away from the method behind the magical effect, and toward the magical effect itself. If the magician wants the spectators’ eyes (and/or attentional spotlight) focused on his face, he may look directly at his audience. If the magician instead wishes the spectators to shift their gaze (and/or attention) to a particular object, he himself may turn his head and eyes toward that object, and the heads and eyes (and/or attention) of the spectators will quickly follow suit (Macknik et al., 2008). Thus, the face of the magician provides effective social misdirection – via joint attention – in many magic illusions. Joint attention is critical for language acquisition and cognitive and social development (Scaife and Bruner, 1975; Tomasello and Farrar, 1986). But it also makes us susceptible to magic tricks that exploit our natural impulse to pay attention to the same places and objects attended by other people around us.

Previous research has found that magicians can effectively use their own direction of gaze to influence the gaze direction of observers (Kuhn and Land, 2006). Here we wondered if gaze misdirection could similarly improve the perception of a magic illusion not previously studied in the laboratory, which involves the simulated toss of a coin from hand to hand, and its subsequent perceptual vanish. In contrast to the previous studies (Kuhn and Land, 2006), we found that the magician’s gaze misdirection did not intensify the subjects’ perception of the illusion. Our data suggest that there is no simple “one size fit all” solution concerning the effects of social misdirection on the perception of magic, and that different magic illusions may be enhanced, unchanged, or lessened by social misdirection, in ways that remain to be explored.

The specific types of social misdirection studied may additionally explain some of the discrepancy between the current findings and Kuhn and Land’s (2006). In Kuhn and Land’s study, the magician’s fake throw was conducted under two conditions of “social cueing”: a pro-illusion condition in which the magician’s eyes and head followed an imaginary ball moving upward, and an anti-illusion condition, in which the magician looked at the hand concealing the ball. In the current study, the magician either looked at the camera or his head was blocked. These two conditions are complementary to the ones used by Kuhn and Land, in that their magician looked either to the simulated position of the ball, or to the actual position of the ball, thus the magician’s gaze was never neutral with respect to the ball. The inclusion of a “socially neutral” gaze condition could have involved the magician closing his eyes, or blocking the magician’s eyes and head (as in the current study). Future research should ideally combine both experimental approaches, incorporating pro-illusion and anti-illusion conditions, but also conditions that eliminate or neutralize the potential effects of social misdirection.

The proficiency of the magician performing this trick may be a factor. Magic theorist Ascanio (2005) stated that a magician should strive for such degree of dexterity that no misdirection should be necessary, and such effective misdirection as to negate the need for high dexterity. Mac King may perform this sleight with such skillfulness that the illusion is already optimized without the addition of social misdirection (Max Maven, personal communication). Cavina-Pratesi et al. (2011) found that the kinematics of a magician’s simulated grasp are very close to those of an actual grasp, and that magicians’ simulated actions do not show many of the typical kinematic biases usually seen with pantomimed actions by non-magicians. Here we found that naive observers required a large amount of exposure to real and simulated coin tosses to distinguish most effectively between the two (20 trials combined; Figures 1 and 2). Our video recordings of Mac King performing real and simulated tosses moreover indicate that Mac King’s timing of a simulated toss matches the timing of a real toss with great accuracy (∼235 ms in the Magic Trick condition, ∼269 ms in the Real Toss condition). Thus, one might conclude that social misdirection is redundant for this particular magic trick, but only if performed by a master magician.

One counterargument is that subjects were able to overcome the illusion eventually, despite Mac King’s mastery. Around the 10th trial, Mac King’s sleight-of-hand technique was no longer sufficient to maintain the illusion, whether his face was covered or not. Had the facial cues been effective as misdirection, the illusion would have persisted for more repetitions in the Face Visible condition than in the Face Occluded condition. This was not the case. It follows that if a less skilled magician were to perform this trick with imperfect sleight-of-hand, facial cues may not enhance the illusion either. If so, one practical recommendation to magicians performing this sleight would be to execute the toss without lifting their eyes to the audience, but to keep their gaze trained on the supposed location of the coin at any given time, so as to maximize the audience’s attention to the illusory coin (via joint attention) and thus enhance the feeling of magic when the coin “vanishes” from the conjuror’s hand. Future research should determine the effectiveness of social misdirection for this and other magic illusions, as executed by magicians with varying degrees of ability.

The current study focused on gaze misdirection as a potentially powerful source of joint attention. Future work should address the comparative effectiveness of the various forms of joint attention/social misdirection (i.e., gaze/head direction, body orientation, verbal cues, etc.) on the perception of this and other magic illusions.

The magician’s axiom “Never do the same trick twice” indicates that if a magician were to perform the same trick twice for the same audience, there would be an increased chance that the audience would identify the underlying method and figure out the trick (King, 2007; Macknik et al., 2008). Several previous studies have shown that magic tricks are more likely to fail when observers view them a second time (Kuhn and Tatler, 2005; Kuhn and Land, 2006; Tatler and Kuhn, 2007; Kuhn et al., 2008). Similarly, many inattentional blindness demonstrations are a one-time only kind of effect. For instance, observers are more likely to detect a gorilla among basketball players if they watch the video for a second time (Simons and Chabris, 1999; Simons, 2010). Our current results indicate that some magic tricks are very resistant to repeated viewing, requiring many more than two performances to lose their effectiveness entirely.