Two players observe a Poisson stream of offers. The offers are i.i.d.r.v.s from $U_{[0,1]}$ distribution. Each player wants to accept one offer in the interval $[0, T]$ and aims to select an offer larger than the opponent's one. Offers arrive sequentially and decisions to accept or reject must be made immediately after the offers arrive. Players have equal weights, so if both players want to accept a same r.v., a lottery is used to the effect that each player can get it with probability $1/2.$ If one player accepts a r.v. and the other doesn't the latter player waits for a larger r.v. appearing before time $T.$ Call this event his win. Each player wants to maximize his probability of winning. The normal form of the game is formulated and the explicit solution is given with Nash values and equilibrium strategies. The bilateral-move version of the game is also analysed and the explicit solution is found. It is shown that the second mover stands unfavorable, on the contrary to the case in multi-round poker.