Each iteration of HB produces a candidate "draw" for each respondent, which is a vector of utilities that represent one realization of the possible preferences for that individual. The next iteration may produce a different "draw" for that respondent which is actually somewhat different from the previous draw. Across hundreds and thousands of draws, if you were to plot a histogram of a single part-worth utility for a single level of an attribute, you will notice a quite normal distribution. The variance of this distribution represents the degree of uncertainty we have about this respondent's preference and its mean represents our best guess of this respondent's preference score.

If we were to use just one draw per respondent after convergence was obtained (after the burn-in period), we would get a pretty noisy view of our data, since the draws have a substantial amount of variance around their true means. Only after 100s or preferably thousands of draws accumulated (after convergence is assumed) per respondent would we obtain a stabilized view of the mean and distribution of uncertainty around each respondent's preferences.

Out of convenience, practitioners have typically just taken the collapsed mean for each respondent (the mean of the draws, also called the "point estimates") across the 1000s of "used" draws after the burn-in period. This historically has been easier to deal with from a memory and data processing time standpoint. However, Bayesians would argue that the more correct way to use the data is to simulate preference shares based on the 1000s of draws after convergence.

Randomized First Choice is a middling position, allowing for the convenience and ease of data storage due to using the point estimates, but simulating draws of uncertainty for each respondent around those means. Randomized First Choice also imposes an extra degree of correlation among "similar" product concepts, leading to greater penalty for "me-too" imitation products.