My first question is - how much are you planning to gamble / lose ? Avg bet per hand / for how long ?
If you received a specific mailing offering to reimburse you airfare it should be specified on the offer.
In the past when I have gotten airfare comped all I had to do is take my ticket/receipt to the cashier, they made a call to my host and they gave me my money - I have also gotten mailers stating they will reimburse me a set amount when I arrive and show my airline ticket - the amount varied from $150 - $350.
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