The evidence from the Qu'ran includes this (from islamqa):
“O you who believe! Intoxicants (all kinds of alcoholic drinks), and gambling, and Al-Ansaab [stone altars set up for sacrifices to idols etc], and Al-Azlaam (arrows for seeking luck or decision) are an abomination of Shaytaan’s (Satan’s) handiwork. So avoid (strictly all) that (abomination) in order that you may be successful".
Scholarly opinion has:
“When chess distracts us from what we are obliged to do both inwardly and outwardly, it is haraam according to the consensus of the scholars – such as when it distracts from an obligatory duty such as prayer or anything that is necessary in the interests of oneself or one’s family, or enjoining what is good and forbidding what is evil, or upholding ties of kinship or honouring one’s parents, or any obligations connected to positions of authority or leadership, etc. In this case it is haraam according to the consensus of the scholars. Similarly, if it involves anything that is haraam such as telling lies, swearing false oaths, cheating, wrongdoing or helping in wrongdoing, or other forbidden things, then it is haraam according to the consensus of the Muslims.”
*(Adapted from Majmoo’ al-Fataawa, 32/218, 240). *
Al-Dhahabi (may Allaah have mercy on him) said: “With regard to chess, most of the scholars say that it is haraam to play it, whether that is for money or not. If it is played for money then it is indisputably gambling. Even if it is not played for money it is still gambling and haraam, according to most of the scholars… al-Nawawi (may Allaah have mercy on him) was asked about playing chess, is it forbidden or permissible? He (may Allaah have mercy on him) replied that if it makes a person miss praying on time or he plays for money, then it is haraam, otherwise it is makrooh according to al-Shaafa’i and haraam according to others…” (al-Kabaa’ir, 89-90).
However, I do not understand why Al-Dhahabi says that when chess 'is not played for money it is still gambling'; my understanding of gambling is the kind of risk involved and the association of money.
In short: Its gambling that is haram; in particular dice & board-games have been associated with gambling, so by extension one may think that these games are then haram; but the actual connection is not there; they are maqrooh;