The first algo maximizes happiness (always choosing pizza is the happiest choice in aggregate 0.6*1+0.4*0+0.1*0 = 0.6), while the second maximizes equal chances

The first algo maximizes happiness (always choosing pizza is the happiest choice in aggregate 0.6*1+0.4*0+0.1*0 = 0.6), while the second maximizes equal chances for everyone (0.6^2+0.3^2+0.1^2 = 0.46). You can't directly compare things that maximize different objectives.