So in chapter 2, David finally becomes king officially. However, at apparently around the same time, Abner decides to declare Saul's son Ishbosheth the king. No doubt Abner, being a close relative of Saul, would prefer to keep the monarchy in the family.
This does present a problem for the SAB though, in that according to 1Chronicles 10, "all [Saul's] house died together" during the battle that saw the death of Saul. One of the things that can be said in reply to this is that it may not be clear what comprises Saul's "house". It's well established elsewhere that at least one of Saul's grandchildren is alive, and as I just said above, Abner is a relative of Saul. One might consider the idea that his "house" is his royal line, but even that is problematic, as Ishbosheth not only survives, but briefly sits on the throne. It might also be that Saul's "house" refers to men in his family of the proper age to fight in wars, but since Ishbosheth is somewhere around forty years old when Saul dies, this seems highly unlikely. While one can also sometimes find some ambiguity in the word "together", I don't think that's going to suffice here either, as clearly Isbosheth lives at least two years after Saul's death. The only real room for ambiguity in the language here that I can see is in the word "son", which as has been mentioned several times is a much more fluid word in Hebrew, capable of referring to any descendant. If Ishbosheth was Saul's grandson, perhaps there is no contradiction, but there's really no indicator of such an idea other than the fact that it might solve this issue, and that Ishbosheth doesn't seem to ever be mentioned until this point. In short, I don't know what to make of the claim of 1Chronicles 10:6.
A strange story follows. The armies of David and Ishbosheth meet together in Gibeon, and Abner suggests "Let the young men now arise, and play before us." The play turns out to be lethal, and in short order, twenty-four men are dead. Is this a "cruel game" as the SAB says? Maybe. The way it sounds to me is that the idea was to have a relatively non-violent wrestling match, and it turned sour, as every single one of the men was set on treachery against their opponent. Indeed, this is a violent event, and one that doesn't make much sense, especially since there are no formally declared hostilities between these two armies.
The next notable event in the plot is Abner's killing of Asahel, the brother of Joab. This seems to be clearly a case of self-defense, as well as a killing in the midst of battle, and yet Joab later seeks revenge for this act. Once all the fighting is done on this particular day, Ishbosheth's soldiers lose 360 men, while David loses only 20.