@article {24405,
	title = {The Big Match with a clock and a bit of memory},
	journal = {Mathematics of Operations Research },
	year = {In Press},
	abstract = {The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his\&nbsp;hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise\&nbsp;he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future\&nbsp;stage.The undiscounted Big Match has been much-studied. Blackwell and Ferguson (1968) give an epsilon-optimalstrategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire\&nbsp;past history. Any strategy that depends on just the clock or just a finite memory is worthless (i.e., cannot\&nbsp;guarantee strictly more than the least reward). The long-standing natural open problem has been whether every strategy that depends on just the clock and a nite memory is worthless.The present paper proves that there is such a strategy that is epsilon-optimal. In fact, we show that just two\&nbsp;states of memory are sfficient.},
	author = {Kristoffer A. Hansen and Rasmus Ibsen-Jensen and Abraham Neyman}
}
