State-run lotteries are ALWAYS about the transfer of wealth and property from the poor and marginalized to the wealthy and connected. This was true during colonial times, this was the manner by which the state of Georgia divvied up land stolen via Indian removal, culminating in 8 substantial (and all rigged) lotterying of land that can only be characterized as stolen under the threat of muskets and bayonets. It's not a coincidence that lotteries became increasingly unpopular. This was then deliberately conflated with private lotteries ran by blacks, immigrants, and the poor where the house odds were good but not anywhere close - to the tune of 1 in 900 compared to 1 in 14 million or so for your typical 6 out of 49 game, made a moral issue, then a tax issue (giving more reason to raid minority neighborhoods), until the 1970s when essentially states began seeing the system as a two-birds-one-stone scenario both in raising revenue and also booting out what was otherwise an illegible parallel society that it had little direct way to profit from or exercise control over.
The really interesting counter-example - or really, the most incompetent series of lotteries ever ran by a state - was the excise farming schemes the British colonial administrators ran in SE Asia, in particular Penang and Singapore and further afield in Malaya, between the 1840s and officially 1903. Excise farming is basically the lotterying of monopolies on the vice trade for fixed periods of time, which existed since the 1500s and periodically gets brought out (prominently under Cromwell, and a bit during the restoration), except because the decline of the East India Company and the lack of civil servants and administrators who had a working knowledge of Chinese, which had become the biggest financial players and essentially realized that the authorities were unable to make sense of the place-of-ancestral-origin system that had little to do with what the British were familiar with (like blood quantum) and inadvertently enabled the same native-place association or Landsmannschaft (we need an English word for this, btw) to simply dominate certain vice trades by the simplest subterfuge - by leveraging the comparatively fluid role personal names represented. Yes, it took more or less an actual case of "all Asians look alike" for a state lottery to fail. Carl Trocki's works are the authoritative research on this subject and time period for those interested in what probably represents one of the most mind-boggling peacetime self-owns by two successive governments that in mainstream academic discourse (outside Subaltern, Asian, and Diaspora/Migration studies, which are arguably niche and very much interdisciplinary), represents the archetype for hegemonic power relationships in practice. I suppose one can also chalk it up as a lottery win there, a rare one, but someone does usually actually win the lottery eventually.