Alcohol Dehydration: Carbenium Ion Intermediate

The elimination of water upon protonatin of 2,3-dimethyl-2-butanol generates the 2,3-dimethyl-2-butanium ion, a tertiary cation. The cleavage of the C-O bond on the protonated alcohol requires only about 22.8 kcal/mol. The protonated alcohol is best seen as a water-solvated carbenium ion; hence, the loss of water is more a desolvation than the breaking of a covalent C-O bond. The cation can loose a beta-hydrogen as a proton to form an alkene. There are beta-hydrogen atoms available on 2 methyl groups as well as on the isopropyl group. Which kind of hydrogen is more likely to be eliminated?

Figure. The MP2(full)/6-31G* optimized structure of 2,3-dimethyl-2-butanium ion.