How many times must I beat the mysterious monk in the inn at Dice Poker to get his relic?

It turns out that neither a sum of money nor a streak of victories is the trigger for earning his "relic"; instead, you must win against the monk in Dice Poker with a dice hand of two pairs. This requires a fair amount of luck, since the only hand two pairs beats is one pair or two pairs of a lower total sum. If you're worried about losing money, save/loading before playing him is effective.

The reward for this is a link in the Extras menu to a site which also acts as a link to a discount on 11 different Atari games, including Outcast, Master of Magic, Independence War 2, and Master of Orion 1+2. The site that this link went to is now defunct and redirects to a spam site, and I'm not sure if this option is available anymore in the game since the special offer has concluded.