Selection Bias when Evaluating the Board

Board cards in real Hold 'Em games (as opposed to theoretical probabilities) face some sort of selection bias -- but we are unable to conclude the impact of this yet.

What do we mean by "selection bias?"

Many studies can suffer from this. For example, if you run a poll via e-mail to determine conclusions about the populace at large, you might experience selection bias. This survey groups is unlikely to be representative of the population as a whole, since it is more likely skewed toward those middle-class and up who are more likely to have internet access. I would also be skewed toward a younger demographic more willing to participate in an online survey.

We can't yet prove that this impacts poker Hold 'Em boards, but we have an early hunch that it does. One example may be that actual five card boards are slightly less likely to have an ace show because of a long-run trend for those hands played out to showdown to include one or more players holding an ace.

If hands played to showdown are more likely to be hands where players are holding aces, then the board is less likely over the long run to match the theoretical number of aces showing up.

Similarly, it is possible that more five-card boards show flushes at a very small statistical increase over the theoretical probability numbers. Because when a flop shows two cards of the same suit, it might be feasible that some players may call to showdown when they would otherwise fold earlier.

Early folds mean less river cards are dealt (and not included in our sample.) Players who call down with flush draws may give a slight statistical bump to flush probability.

Also -- the stakes in poker hands will probably influence board cards. If the average online mid to high stakes limit hold 'em game has many less hands played to showdown and more pre-showdown folding, then the board results might also differ from theoretical probabilities. Especially if all that is being evaluated are full 5-card boards.

Note: This was first posted as an addendum to a prior post. Edited to make it a standalone post.