31. Nothing the medical/psychological nature of problem gambling behaviors, the letter said that before being readmitted to the casino he would have to present medical/psychological information demonstrating that patronizing the casino would pose no threat to his safety or well-being.

【分析】多重复合句。句子主干为the letter said that...引导宾语从句。Noting…为现在分词作伴随状语；宾语从句主干为he would have to present medical/ psychological information,其中 before being readmitted to the casino作时间状语，现在分词结构demonstrating that …作 information 的后置定语，其中包括that引导的宾语从句作demonstrating的宾语。

【译文】在说明不良赌博行为对人生理或心理上的危害的同时,信中还指出：在他被重新允许光顾赌场之前，他 (威廉姆斯）必须出示生理或心理状况的相关信息，以证明光顾赌场不会对他的人身安全和健康造成任何威胁。
【点拨】1)note在本句中是“指出，提到”的意思。此外,作动词时,还有“记录;注意，留意”的意思。2)patronize“以高人一等的态度对待;光顾;赞助，资助”。

32. Nevertheless, Williams' suit charges that the casino, knowing he was "helplessly addicted to gambling"，intentionally worked to "lure" him to "engage in conduct against his will".

【分析】多重复合句。句子主干为Williams' suit charges that…，that引导宾语从句。宾语从句主干为the casino…worked to "lure" him to…；knowing…为现在分词结构作伴随状语，其中包含一个省略了引导词的宾语从句。
【译文】然而，威廉姆斯的案件控诉这家赌场明知他“无法自拔地沉溺于赌博”，仍有意地“诱使”他“违背自己的意愿，参与赌博”。
【点拨】be addicted to “沉溺于，对…上瘾”。同义表达还有 abandon/addict oneself to, be given to, indulge in, wallow in等。