"If I were to put a pound into the lottery each week, would not my chance of winning a fortune also need to be counted as part of my wealth"
I'm not an economist, but I'm guessing the answer is yes. So your wealth would increase by one thirteen-millionth of the average jackpot (about £5 million-ish?), and decrease by £1. No?
(obviously we'd also need to factor in the other prizes, and odds of winning them, but my point is that statistically you'll lose money on the lottery, so your wealth must decrease with the purchase of a ticket, albeit by slightly less than the cost of the ticket)