Not much. A neat new paper in Political Psychology by Doherty, Gerber, and Green finds that winning the lottery decreases support for the estate tax. But there is only weak evidence that lottery winners favor less redistribution, or are more pro-market generally. Winning the lottery...
...has little impact on broad orientations toward social stratification. Only one of the general items(ironically, the item that asks whether those in high positions have special abilities)
comes close to statistical significance, and three of the four general items generate unexpectedly negative coefficients. Much more powerful and statistically robust is the relationship between lottery prizes and views about estate taxes.
No surprise to opponents of the Self-Interested Voter Hypothesis like me. But it's still worth repeating, for the SIVH is a zombie-like theory that refuses to die.