CAPT OF A B737 FAILED TO HOLD SHORT OF AN ACTIVE RWY DURING TAXI OUT AS INSTRUCTED. WHEN HE OBSERVED ANOTHER ACFT AT THE DEP END OF THE RWY HAD STARTED A TKOF ROLL; HE ACCELERATED CLRING THE RWY.

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DEP ATIS AT MSY SAID 'DEPARTING RWY 19.' WHILE WE WERE STILL IN THE CHOCKS; WE HEARD GND CTL OFFER RWY 28 TO ANOTHER ACFT. SINCE THAT IS A MUCH SHORTER TAXI FOR US; WE DID OUR PRELIMINARY TKOF DATA BASED ON RWY 28. AFTER PUSHBACK; ANOTHER ACFT ASKED FOR RWY 28 AND WAS DENIED. TSTMS HAD MOVED TOO CLOSE IN THAT DIRECTION. SO; I FULLY EXPECTED OUR TAXI INSTRUCTION TO BE 'TAXI TO RWY 19.' WHEN WE CALLED FOR TAXI; SURE ENOUGH; I HEARD 'TAXI TO RWY 19.' AT THAT POINT; I MUST HAVE SHUT DOWN MY INTERNAL RECEIVER; FOR THERE WAS AN ADDED PHRASE WHICH I COMPLETELY MISSED: 'HOLD SHORT OF RWY 10.' THE FO HEARD AND READ BACK THE HOLD SHORT INSTRUCTION (I MISSED IT AGAIN); AND HE THEN BEGAN RECALCULATING OUR TKOF DATA FOR RWY 19. THE RECALCULATION CAUSED THE FO TO BE HEAD DOWN DURING MY APCH TO THE HOLD SHORT POINT. FOR MY PART; AS SOON AS I 'HEARD' WHAT I EXPECTED TO HEAR; I SWITCHED MY ATTN TO 3 OTHER THINGS. AS I TAXIED; I BEGAN TURNING THE RADAR AND FORMULATING A WX ESCAPE PLAN. I SIMULTANEOUSLY DISCUSSED WITH THE FO BLEED AIR AND FLAP CONFIGNS FOR OUR HVY ACFT ON A FAIRLY SHORT WET RWY. I WAS ALSO PREPARING A ROUGH MENTAL DRAFT OF A PRE TKOF ANNOUNCEMENT TO WARN THE PAX ABOUT THE IMPENDING TURB AND TO KEEP THE FLT ATTENDANTS SEATED DURING THE CLBOUT. AS I APCHED RWY 10; I SAW AN ACFT IN POS AT THE OTHER END. I ASSUMED HE WAS IN POS AND HOLD; SINCE I 'HAD' CLRNC TO CROSS. TO MY HORROR; AS I CROSSED; I SAW THE OTHER ACFT START ROLLING. I ADDED PWR AND GOT QUICKLY OUT OF THE WAY. IN THE PAST; I HAVE ALWAYS SAID ALOUD ANY HOLD SHORT INSTRUCTION JUST TO REINFORCE IT TO MYSELF. FROM NOW ON; I WILL ASK MY FO'S TO ENSURE I REPEAT THE HOLD SHORT INSTRUCTION. ADDITIONALLY; I WILL BE MUCH MORE SENSITIVE TO THE PROB OF 'HEARING WHAT YOU EXPECT TO HEAR.'