 Another group of games of the same general family as Lorenzen’s are the proof games of Pavel Pudlak 2000. Here the Opponent (called Prover) is in the role of an attorney in a court of law, who knows that the Proponent (called Adversary) is guilty of some offence. Proponent will insist he is innocent, and is prepared to tell lies to defend himself. Opponent’s aim is to force Proponent to contradict something that Proponent is on record as having said earlier; but Opponent keeps the record and (as in the pebble games above) he sometimes has to drop items from the record for lack of space or memory. The important question is not whether Opponent has a winning strategy (it’s assumed from the outset that he has one), but how much memory he needs for his record. These games are a useful device for showing upper and lower bounds on the lengths of proofs in various proof systems.