Winner Determination: Bankroll Instant Run-off

The bankroll instant run-off winner determination rule was first used during the 2007 Annual Computer Poker Competition.  In contrast to series instant run-off, bankroll instant run-off uses an agent's total bankroll score to knock out an agent in each elimination round.  Both instant run-off variants favour equilibrium play, as an agent which can't be exploited is likely to end up in the middle of the ranking at each iteration, where it is not eliminated.  Using total bankroll instead of points for win/ties/loss has two advantages: there is no need determine if every possible combination of agents is a win/loss or a tie, and the extension of bankroll instant run-off to multi-player games is easy and conceptually simple.

Heads-up Bankroll Instant Run-off

The bankroll instant run-off technique is implemented recursively:

  1. Initialize the set of remaining agents S to be all agents.
  2. Consider all matches between agents in S, and compute the total bankrolls of each agent
  3. Define T to be the agents with the lowest total bankroll. These will be ranked below the other remaining agents in S, and tie with each other. Remove T from S
  4. Repeat 2 and 3 until S is empty

3 Player Bankroll Instant Run-off

We generalize the two player instant run-off bankroll winner determination rule as follows:

  1. Initialize the set of remaining bots S to be all bots.
  2. Play all possible m choose 3 matches between bots in S, where m is the size of S, and compute the total bankrolls of each bot
  3. Define T to be the bots with the lowest total bankroll. These will be ranked below the other remaining bots in S, and tie with each other. Remove T from S
  4. Repeat 2 and 3 until S is contains only 3 bots
  5. Play a match between the last 3 bots, and compute the total bankrolls of each bot
  6. The last 3 bots come first, second and third based on their total bankroll from this match