It could be further generalized that on an infinite timeframe gambling on a 50% win chance with a finite bankroll inevitably ends in a bust of one of the players. This is what I would call a statistical certainty
So let me draw these conclusions . Assuming that there is no house edge or in the case of two people tossing coin game with exactly 50% chance for each player, Also
finite bankroll and infinite time to playThere would be several
conclusion outcomes after X number of game
1. Each player's bankroll would remain the same
2. One player will have higher bankroll and another with lower bankroll than what they started with
3. One would be the winner while one bust
These are not conclusions, these are possible outcomes
So Are there any other possible outcomes aside from those three?
It isnt 100% certainty that one will bust while one win because at exactly 50% chance to win with no edge, no one could tell how things will be after several number of games
We are talking statistics here
It doesn't matter what the outcome will be in a few games
Not just few games, I wrote X number of games in the previous post so it could be any number.
after just one bet, there'll already be an edge in the form of a bigger balance because one player necessarily loses and the other necessarily wins.
Having bigger balance is not an edge against the smaller balance player. If the wager amount stays the same each round, bigger balance player will just have longer time to lose everything compared with smaller balance assuming that those player keep losing
And technically, if they wager all, there is 100% certainty that one of the players will bust. Since bankrolls are finite, this can be the case on an infinitely long timescale as well
There is no certainty in exactly 50% chance game, as I have written before there are 3
conclusions outcomes in finite bankroll and infinite timescale