Fire controls tree cover in many savannas by suppressing saplings through repeated topkill and resprouting, causing a demographic bottleneck. Tree cover can increase dramatically if even a small fraction of saplings escape this fire trap, so modeling and management of savanna vegetation should account for occasional individuals that escape the fire trap because they are "better" (i.e., they grow faster than average) or because they are "lucky" (they experience an occasional longer-than-average interval without fire or a below-average fire severity). We quantified variation in growth rates and topkill probability in Quercus laevis (turkey oak) in longleaf pine savanna to estimate the percentage of stems expected to escape the fire trap due to variability in (1) growth rate, (2) fire severity, and (3) fire interval. For trees growing at the mean rate and exposed to the mean fire severity and the mean fire interval, no saplings are expected to become adults under typical fire frequencies. Introducing variability in any of these factors, however, allows some individuals to escape the fire trap. A variable fire interval had the greatest influence, allowing 8% of stems to become adults within a century. In contrast, introducing variation in fire severity and growth rate should allow 2.8% and 0.3% of stems to become adults, respectively. Thus, most trees that escape the fire trap do so because of luck. By chance, they experience long fire-free intervals and/or a low-severity fire when they are not yet large enough to resist an average fire. Fewer stems escape the fire trap by being unusually fast-growing individuals. It is important to quantify these sources of variation and their consequences to improve understanding, prediction, and management of vegetation dynamics of fire-maintained savannas. Here we also present a new approach to quantifying variation in fire severity utilizing a latent-variable model of logistic regression.