Electroencephalogram (EEG) phase can capture neural oscillation dynamics. Accordingly, EEG phase is a potential target for neurofeedback and brain-computer interfaces (BCIs). However, rigorous tests of the generalizability of real-time EEG phase are needed, requiring accurate phase estimates. We examined how cognitive states affect EEG phase prediction accuracy in the parieto-occipital alpha band. We identified datasets through public repositories. After preprocessing, we used the Educated Temporal Prediction Algorithm (ETP) to predict future peaks. We compared these predictions to the original signal, and defined accuracy from 0 to 100%. Our independent variable was cognitive state (eyes-open rest, eyes-closed rest, task), dependent variable was accuracy, and covariates were EEG instantaneous power and signal-to-noise ratio (SNR). We used a linear mixed-effects model, with random effects for dataset and individual. Across the 11 datasets, we had 543 participants and 1,641,074 predictions. There were no significant accuracy differences among the conditions (p < 1e-5), with a baseline accuracy of 59.07%. Power had an effect on accuracy, with a unit increase leading to a 13.1% increase in accuracy (p < 1e-5). SNR had an effect on accuracy, with an effect size of 0.46% (p < 1e-5), with a significant negative interaction with power with an effect size of -0.51% (p < 1e-5). Our results indicated that we could predict EEG phase accurately across cognitive conditions and datasets, with higher accuracy for high instantaneous band-power and SNR. Accordingly, real-time EEG phase experiments, closed-loop technologies, and BCIs should minimize external unwanted noise while targeting periods of high power, as opposed to manipulating experimental and cognitive conditions.