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The general thought, though opinions differ, is that airline miles are worth about $.02 per mile, and Marriott Rewards points about half that. However airline miles become more valuable if used towards 1st class/business class upgrades or tickets than if used to obtain coach tickets. Marriott Rewards points also become more or less valuable depending on how you use them. Most folks here feel the most valuable usage of Marriott Rewards points is to obtain a "travel package". These packages are listed on the Marriott website. Generally, the travel packages provide 7 days at a Marriott property plus a certain amount of frequent flyer points on your choice of airline (including American). The amount of frequent flyer miles you receive depends on the number of Marriott Rewards points you spend for the travel package. One of the advantages of the travel package is that as you increase the Marriott points you are spending for the package, you get a one to one value of Marriott point to frequent flyer mile rather than the common perception that the airline mile is worth twice the Marriott point.

As to credit cards, you may want to carry both. The Marriott Visa is free the first year, inexpensive after that, and provides significant bonus miles if used at Marriott properties. However, the Marriott Visa would be inferior to use for other than Marriott purchases because spending a dollar only provides one point, while spending a dollar on an airline card provides one mile, which is worth more than one Marriott point.

Another alternative might be to consider the new Diners Club Master Card which, for $95 per year, gives you one mile per dollar on any airline, including American. If you want to start collecting British Air miles, you are likely to be provided bonus opportunites to get 1.5 miles per dollar. The Diners card also provides primary car rental insurance (rather than the secondary insurance provided by many other cards) and purchase protection/extended warranty, etc. You can see the Diners Club board for various opinions as to that. This new Diners Club card will come out in the next month or so, and I would guess Diners will provide a significant bonus for successful application.