Preflop Hand Income

A 13*13-matrix is shown. The Deuce cards are to the left/top, the Aces to the right/bottom. Thus, the right/downward diagonal displays the pairs. Red color means a positive income, whereas blue color indicates a loss (in a game where each player calls the blinds and then checks all further bets). Clearly, a pair of two Aces is a good hand to start. Above the diagonal, the suited card pairs are shown, below the diagonal, unsuited pairs. Thus, the pixel in the upper right corner shows the income for a Deuce/Ace suited pair.

Papp already describes the apparent tendency to prefer big cards for larger player groups. From the graphic, it becomes evident that also hand pairs being suited or connectors become more important. This can be explained by to the fact that the income is counted rather than the chance to win a single hand (for larger tables, a single win will produce much more revenue than a win in a heads-up game if the same amount is bet by each player). However, it takes a stronger hand to win, thus favouring straights and flushes. Therefore, connector cards (adjacent to the diagonal) become more important, and you can loose your money easily by playing with non-pair unsuited cards.

Note that the income is the result of a Monte-Carlo-simulation rather than an exhaustive enumeration. I used a million games per hand/player combination, but still some minor irregularities (as can be seen for unsuited pairs with an Ace (bottom line of the graphics) for larger player numbers) exist.

Preflop calls

This graphic shows the percentage of hands played at the various positions. Position 1 is the small blind, position 2 the big blind, which obviously play far more hands. The benefit of later positions can be seen, since it seems more tempting to call a hand at a later position, but it does not amount to much. The difference of the 11/12-player games may originate from the data, there were only a small number of such games. Funny enough, position 3, which is the first to make an actual decision, seems to call more often than later positions do, althought common Poker knowledge dictates that this is actually the worst position to have.

The following graphic shows the hole cards that got played to showdown. Of course, this is not exactly the number of hands that entered preflop betting, but those that didn't fold until showdown.

Actually, that is seems that those guys at the IRC channel have yet to read their Sklansky. There seems to be little special emphasis on suited cards, and low pairs are way too common. Recall that this is only the cards that reach showdown - suited cards that have not met their flush will be folded by now (here, suited cards are in the lower triangle).

This graphic shows the preflop activity, i.e. the number of raises. It is not very exact and the data is not very conclusive, but it seems that both very strong and very weak hands get lots of action. The latter may be explained by the fact that they are played by the blinds only, and those always have at least two actions during preflop ("Bc"), hence the apparently heavy action during preflop. I need to adapt the data here -- consider it corrupted by now.