If the state of Nature is \(y\in R^ 1\) and the decision of the Statistician is \(x\in R^ 1\), then the gain is \(h(y)I_{(-\Delta /2,\Delta /2]}(x-y),\) where \(\Delta\) is a given number. If y is a parameter of a discrete distribution \(p_ j(y)\), \(j=0,1,...,n\), and \(x_ j=x(j)\) is the decision when j has been observed, then \[ H(x,y)=\sum^{n}_{j=0}h_ j(y)I_{(-\Delta /2,\Delta /2]}(x-y) \] is the expected gain, where \(h_ j(y)=h(y)p_ j(y)\). Estimation of the value of the game with the pay-off H(x,y) as well as the best strategies for both players, if \(h_ j(y)\geq 0\) are continuous functions, are discussed.