I'm not sure it was Jacks ego that made him play those games of cards. He saw it surely merely as a means to win back his medicine. I don't think he see's Sawyer as a threat, more as a thorn in his side and not necessarily someone he needs to measure up to.
The person Jack has ego trips with is Locke. Locke is so much more of a competition to Jack and I'm sure Jack feels threatened by him and this is why he always needs to be one up on him.
Regarding Ana Lucia, I know you are concerned about your lady there KoR-evo, but if she can bring her team through the 48days of hell, whilst trying to keep one step ahead of the others, she is more than capable of a little trek into the jungle with Sayid and Charlie. I bet Jack saw it that way too.
