A waste-gate valve device, comprising: a turbine housing comprising a waste-gate channel through which exhaust gas bypasses a turbine; and a waste-gate valve configured to open and close an outlet of the waste-gate channel, the waste-gate valve comprising a valve body configured to open and close the outlet of the waste-gate channel, and a protrusion configured to be housed in the waste-gate channel when the valve body closes the outlet of the waste-gate channel, wherein the waste-gate channel ensures a maximum flow rate of exhaust gas at a time when the waste-gate valve is fully open, wherein a flow-path cross-sectional area ratio of the waste-gate channel to a merging portion is not more than 0.2, the merging portion being a portion at which exhaust gas having passed through the turbine merges, wherein a widened portion is disposed on the outlet of the waste-gate channel the widened portion being gradually widened so as to form a curve in cross section and having a flow-path cross sectional area which gradually increases, wherein the protrusion includes a pressure-receiving portion (28A, 48A) configured to, when the waste-gate valve is opened, receive a pressure of exhaust gas flowing through the waste-gate channel, in a region close to a shaft supporting the waste-gate valve, and a reducing portion (28B, 48B) configured to reduce the flow of exhaust gas flowing through the waste-gate channel, in a region remote from the shaft, wherein a flow-path diameter D 1 of the waste-gate channel satisfies a following expression 1, with respect to a relationship to a flow-path diameter D 2 of the merging portion, D 1 ≤ 0.469 × D 2 − 0.5 mm an outlet diameter D 3 of the widened portion satisfies a following expression 2, with respect to a relationship to the flow-path diameter D 1 of the waste-gate channel, D 3 ≥ 1.049 D 1 and wherein the pressure-receiving portion (28A, 48A) is formed in an arc shape which forms a recess portion between the pressure-receiving portion (28A, 48A) and the reducing portion (28B, 48B), as seen from the side of the waste-gate channel. a turbine housing comprising a waste-gate channel through which exhaust gas bypasses a turbine; and a waste-gate valve configured to open and close an outlet of the waste-gate channel, the waste-gate valve comprising a valve body configured to open and close the outlet of the waste-gate channel, and a protrusion configured to be housed in the waste-gate channel when the valve body closes the outlet of the waste-gate channel, wherein the waste-gate channel ensures a maximum flow rate of exhaust gas at a time when the waste-gate valve is fully open, wherein a flow-path cross-sectional area ratio of the waste-gate channel to a merging portion is not more than 0.2, the merging portion being a portion at which exhaust gas having passed through the turbine merges, wherein a widened portion is disposed on the outlet of the waste-gate channel the widened portion being gradually widened so as to form a curve in cross section and having a flow-path cross sectional area which gradually increases, wherein the protrusion includes a pressure-receiving portion (28A, 48A) configured to, when the waste-gate valve is opened, receive a pressure of exhaust gas flowing through the waste-gate channel, in a region close to a shaft supporting the waste-gate valve, and a reducing portion (28B, 48B) configured to reduce the flow of exhaust gas flowing through the waste-gate channel, in a region remote from the shaft, wherein a flow-path diameter D 1 of the waste-gate channel satisfies a following expression 1, with respect to a relationship to a flow-path diameter D 2 of the merging portion, D 1 ≤ 0.469 × D 2 − 0.5 mm an outlet diameter D 3 of the widened portion satisfies a following expression 2, with respect to a relationship to the flow-path diameter D 1 of the waste-gate channel, D 3 ≥ 1.049 D 1 and wherein the pressure-receiving portion (28A, 48A) is formed in an arc shape which forms a recess portion between the pressure-receiving portion (28A, 48A) and the reducing portion (28B, 48B), as seen from the side of the waste-gate channel.