Finally, Poirot reveals his reasons for not thinking Alfred should be arrested. It’s not actually the case that Alfred lacks an alibi. To the contrary, he has a very solid, plausible way of proving that he didn’t buy strychnine from Mr. Mace, but he apparently doesn’t want to use this alibi because he doesn’t want everyone to know (or to
think) that he’s having an affair with Mrs. Raikes. In this way, matters of the heart factor into this already complicated case.