/sci/ - Science & Math

>>11437575
Hey /sci/, I'm looking for help from someone who is smarter than myself since I'm not good with statistics.
On World of Warcraft Classic there is a simple gambling game called deathrolling. Two players declare some bet amount, like 5 gold, and one player rolls first. Their roll is a randomly generated number between 1 and 100. The second player then rolls a number between 1 and whatever the 1st player rolled. This continues back and forth until one player rolls a 1. Whoever rolls a 1 first loses.

Quick example:
1st rolls 1 - 100 and rolls 53
2nd rolls 1 - 53 and rolls 32
1st rolls 1 -32 and rolls 6
2nd rolls 1 - 6 and rolls 2
1st rolls 1 - 2 and rolls 2
2nd rolls 1 - 2 and rolls 1. 2nd player lost and owes 1st player 5 gold.

My question is which player has the greater advantage in winning? The 1st player starts with the highest chances of not rolling a 1, however they start with a chance of immediately losing before the 2nd player even rolls.
I wrote something in python really quickly to see what happened and it looks like playing first has a slight advantage, but that could be due to my poor coding or any myriad of issues with the online compiler or random number generator available through python.

Any thoughts or advice on actually calculating what advantage player one has vs player two?