We propose an approximate distribution for the gapped local score of a two sequence comparison. Our method stands on combining an adapted scoring scheme that includes the gaps and an approximate distribution of the ungapped local score of two independent sequences of i.i.d. random variables. The new scoring scheme is defined on h-tuples of the sequences, using the gapped global score. The influence of h and the accuracy of the p-value are numerically studied and compared with obtained p-value of BLAST. The numerical experiments emphasize that our approximate p-values outperform the BLAST ones, particularly for both simulated and real short sequences.