EE (the last outcome is even and the sum is even)

OO (the last outcome is odd and the sum is odd)

OE (the last outcome is odd and the sum is even)

EO (the last outcome is even and the sum is odd)

From EE and OO the game can be terminated in E (end of game with even total) while from OE and EO is O (end of game with odd total) that can be reached.

The first roll of the die places us either in EE or in OO (the sum equals the last outcome): it’s apparent that E is favoured.

PS: the odds for E are 47:35.

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