Gambler's Ruin

What matters more – Your skill or Your starting position?
Let us make the question a bit more concrete using the classic example of Gambler’s Ruin. This example involves two players. Player 1 and Player 2 are both equally skilled and start with 1,000 dollars at their disposal. The players compete in a series of rounds, betting the same amount in each round.
The game ends once a player is "ruined", i.e., the player goes bankrupt. Here are the rules -

• The Players decides on how much money they will bet in each game
• Bet size does not change throughout the entire game
• The players play each other in a round
• The loser hands over the money based on the agreed bet amount to the winner
• Players keep playing rounds till either player has run out of money