He joined the Greeks in the expedition against Troy.  Pausanias in his Description of Greece (2.20.3) says that in Corinth is a Temple of Fortune in which Palamedes dedicated the dice that he had invented.
Expedition against Troy
Agamemnon sent Palamedes to Ithaca to retrieve Odysseus, who had promised to defend the marriage of Helen and Menelaus. Paris had kidnapped Helen, but Odysseus did not want to honor his oath. He pretended to be insane and plowed his fields with salt. Palamedes guessed what was happening and put Odysseus' son, Telemachus, in front of the plow. Odysseus stopped working and revealed his sanity.
The ancient sources show differences in regards to the details of how Palamedes was caused to die and also the actual way in which his death was brought about. 
Odysseus never forgave Palamedes for sending him to the Trojan War. When Palamedes advised the Greeks to return home, Odysseus hid gold in his tent and wrote a fake letter purportedly from Priam. The letter was found and the Greeks accused him of being a traitor. Palamedes was stoned to death by Odysseus and Diomedes. According to other accounts the two warriors drowned him during a fishing expedition. Still another version relates that he was lured into a well in search of treasure, and then was crushed by stones. Although he is a major character in some accounts of the Trojan War, Palamedes is not mentioned in Homer's Iliad.
Other additional information
Ovid discusses Palamedes' role in the Trojan War in the Metamorphoses. Palamedes' fate is described in Virgil's Aeneid. Plato describes Socrates as looking forward to speaking with Palamedes after death. Euripides and many other dramatists have written dramas about his fate.
The three Fates created the first five vowels of the alphabet and the letters B and T. It is said that Palamedes, son of Nauplius invented the remaining eleven consonants. Then Hermes reduced these sounds to characters, showing wedge shapes because cranes fly in wedge formation and then carried the system from Greece to Egypt*. This was the Pelasgian alphabet, which Cadmus had later brought to Boeotia, then Evander of Arcadia, a Pelasgian, introduced into Italy, where his mother, Carmenta, formed the familiar fifteen characters of the Latin alphabet. Other consonants have since been added to the Greek alphabet. Alpha was the first of eighteen letters, because alphe means honor, and alphainein is to invent.
In one modern account, The Luck of Troy by Roger Lancelyn Green, Palamedes really was double-dealing with the Trojans.
- L Schmitz. A Dictionary of Greek and Roman Biography and Mythology, Volume 3. J. Murray, 1873. Retrieved 2015-04-13.
- Apollodorus, Epitome, Apollod. Epit. E.3.7
- Hyginus, Fabulae, 105
- Pausanias 10.31.2, citing the epic Cypria.
- Ovid. Metamorphoses. pp. 13.34–60, 308–312.
- Virgil. Aeneid. pp. 2.81–85.
- Plato. Apology, 41b.
- Hyginus. Fabulae, 277.
- D. R. Reinsch, "Die Palamedes-Episode in der Synopsis Chronike des Konstantinos Manasses und ihre Inspirationsquelle," in Byzantinische Sprachkunst. Studien zur byzantinischen Literatur gewidmet Wolfram Hoerandner zum 65. Geburtstag. Hg. v. Martin Hinterberger und Elisabeth Schiffer. Berlin-New York, Walter de Gruyter, 2007 (Byzantinisches Archiv, 20), 266-276.
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- Palamedes at Greek Mythology Link