Blaise Pascal and David Hume were united by a love of gambling
Pascal's interest was as far as I understand terminated by his conversion to intense Catholicism, inspired by the Jansenism dominant at the convent at Port-Royal in Paris. Port-Royal produced distinguished philosophers like Pierre Nicole and Nicholas Arnaud and educated the great tragedian Jean Racine. Pascal's interests encompassed mathematics, physics, theology, philosophy of religion, metaphysics, epistemology, and social philosophy.
David Hume was sceptical of all revealed religion though valuing moderate religion as a part of civil society. He certainly did not engage in the asceticism that Pascal followed in his later years, and which may have hastened his death.
Though his attitude to religion was instrumental, Hume has a social philosophy similar in some respects to Pascal. For both, organised society and state institutions emerge through convenience rather than from basic principles. For Hume, this is a happy reality, for Pascal it is part of the view that God is absent from the universe, and from human society. For Hume, humans follow self-interest rooted in 'passions' (Hume used the word in a way that covers all psychological motives), and learn to adopt the rules and institutions which enable everyone's self-interest to flourish enhancing commerce and the arts. For Pascal, this is true but is evidence that humans are half angels half beast, who have lost the grandeur which belongs to divine life.
For both, a godless universe lacks certainty. The world is not guided in every respect by divine purposes, those purposes are distinctly absent. For both, there is a sceptical aspect to their philosophy, for without God's immediate presence what guarantee is there that our perceptions are reliable. Both dealt with questions of probability and chance. Science looks like it contains probabilities, though never certainties. However, some aspects of experience do not even lead us to probabilistic expectations about the future.
Gambling is an obvious example. Hume focuses in his work on knowledge, on the throwing of dice. We know there is a one in six chance of any one side being thrown However, there is nothing we can say about which is more probable, experience does not help ıs, because however many times we throw a die, for the next throw it is still a one in six chance for any one side. For Hume, that is the probabilistic nature of the universe in its most extreme aspect. For Hume, induction establishes probabilities for scientific laws of nature. However, since Hume does not think we know at what the future will be, even at the next moment, his induction has a weak basis, and even more so when we consider that induction rests on a continuity over the mind in time, which Hume thinks has not real justification, since we must regard continuous personal identity as a fiction for unifying states of mind at different times.
By his own account, philosophising brought melancholia to Hume which he relieved by gambling. The gambling, the encounter with uncontrollable chance and intrinsically futile attempts to overcome chance, or to play with chance within a framework of play between individuals which enables us to try and control chance.
Pascal saw the universe as governed by physical laws, but for him they lacked foundations. The only foundation could be God who is absent. Like Hume, Pascal contributed to early probability theory, and as with Hume we can see the gambling as resulting a fear of pure chance, the attempt to control pure chance, or the experience of surviving pure chance. Pascal also emphasised that life could be a dream, that ı could be a king dreaming that I am who I think I am. There would be no difference between being a king and the pauper who dreams vividly half the day of being a king. Our own identity is a matter of uncontrollable chance.
Pascal even produced an argument for religious faith (Pascal's wager) based on chance and simple ideas about probability. Famously, he argued that life without faith is despair. If we have faith, and there is no God, we have lost nothing and gained a life with hope; if we do not have faith but God does exist, we will have less happiness in life and we will suffer damnation in the next life. The rational thing therefore is to have faith. It is a mistake to look at the argument in isolation, as this can make it seem weak and self-deceiving, an argument in which we suppress doubt to make life more pleasant. It is just one part of Pascal's argument about belief and his arguments need to be judged as a whole. I would say that on the whole, he is building up a way of thinking in which we can only grasp reality in any way through an idea of God, which may or may not be correct in the end, but is more than a matter of comforting self-deception.
Gambling, anxiety about reality, and the wish to find a way of contolling chance, of experiencing it as part of a rational universe, or of playing with inner anxiety in order to control it are a strong feature of Pascal and Hume. Where would philosophy be without their interest in gambling?