Las Vegas vs Monte Carlo randomized decision tree complexity
As far as I know, this is still open. A very recent paper that mentions these quantities and some bounds is Aaronson et al: Weak parity (see http://arxiv.org/abs/1312.0036). You can also see chapter 14 of Jukna: Boolean funcions and the 1999 (still beats 1998!) survey by Buhrman and de Wolf. Another very recent paper about randomized decision tree complexity is Magniez et al: http://arxiv.org/abs/1309.7565

Finally, a short summary I made for myself last month (without defs):

R2&lt;=R0&lt;=D&lt;=n

D&lt;=N0*N1&lt;=C^2&lt;=R0^2

s&lt;=bs&lt;=C&lt;=s*bs&lt;=bs^2 (new: [Gilmer-Saks-Srinivasan]: there is f s.t. bs^2(f)=O(C(f)))

D&lt;=N1*bs&lt;=bs^3&lt;=(3R2)^3

deg&lt;=D&lt;=bs*deg&lt;=deg^3 (new: [Tal]: bs&lt;=deg^2)

D&lt;=N1*deg

C&lt;=bs*deg^2&lt;=deg^4

Sensitivity conjecture is that s is also polynomially related to other parameters.