UPDATE #2 (8/15/06): Free for 48 hours, 800 points afterwards?
This appears to be the case, at least in Australia. CAG deadite76 found this:
http://www.xbox.com/en-AU/community/news/2006/0816-texasholdem.htm (page is now gone)
Quoted from NeoGAF
I think this is what it is going to look like. Hopefully they will figure out a way to deal with the people who go all in all the time. It looks pretty though and since it's going to be free I'm definitely picking it up!

pic from teamxbox site.
UPDATE: NO LONGER FREE (CheapyD edit)
http://www.joystiq.com/2006/07/20/joystiq-interviews-greg-canessa-of-xbla/
This appears to be the case, at least in Australia. CAG deadite76 found this:
http://www.xbox.com/en-AU/community/news/2006/0816-texasholdem.htm (page is now gone)
Quoted from NeoGAF
Texas Hold ‘em full version download available to gamers for free for 48 hours on Live Arcade
Enjoy poker night every night with friends, family and gamers around the world.
Microsoft isn’t bluffing: Gamers can log onto Xbox Live within the first 48 hours after launch and download Texas Hold ‘em – completely free of charge! This full-featured poker title for Xbox Live Arcade on Xbox 360 will launch on Wednesday, August 23 at 6pm EST.
For 48 hours only – Wednesday, August 23 through to 6pm EST Friday, August 25 – as a special limited-time only promotion, gamers can download and own the game at no charge (for all Xbox Live Gold and Silver members). Starting at 6:01pm EST Friday, August 25, Texas Hold ‘em for Xbox Live Arcade will be available for 800 Microsoft Points.
This title comes equipped with features that can only be found on Xbox 360. Designed to simulate the risk-reward of real poker gameplay, keep gamers honest, and discourage opponents from betting too recklessly, Texas Hold ’em has an innovative new feature called Persistent Bankroll. Your virtual bankroll is tied to your Xbox Live Gamertag and keeps a running tally of your chip count. If you lose all of your chips in a poker game, you’ll have to play lower stakes buy-in games to make back your stack and earn your way to the big tables.
Texas Hold ’em also offers multiplayer support for up to eight gamers, three modes of gameplay (Standard Games, Scenarios and Tournaments), Achievements, extensive online leaderboards, statistics and high-definition graphics. Enjoy poker night every night with friends, family and gamers around the world (please note that this title may not be available in some countries).
In addition to the exciting release of Texas Hold ’em on August 23, gamers can also look forward tonewgame titles and premium downloadable game content on Xbox Live Arcade Wednesdays from August 16 to September 6, including:
* Cloning Clyde Picture Pack, the action adventure/puzzle game created by Wahoo Studios/NinjaBee (developer of the popular Outpost Kaloki X for Xbox Live Arcade), will have four new gamer picture packs available on Xbox Live Marketplace on Wednesday, August 16, allowing gamers to check out more unique pictures of Clyde. Each gamer picture pack: 100 Microsoft Points each.
* Time Pilot, the futuristic fighter pilot classic from Konami, lets gamers fight through different eras like never before. High-definition graphics and enhanced gameplay designed specifically for Xbox Live Arcade makes this version even better than the original from 1982. Gamers can download Time Pilot on Xbox Live Arcade Wednesday, August 30. Available: 400 Microsoft Points.
* Scramble, the classic side-scrolling ‘shoot-‘em up’ coin-op title from Konami, takes off on Xbox Live Arcade. The 1981 classic, widely considered the first ‘multi-level shooter,’ launches on Xbox Live Arcade Wednesday September 6. Available: 400 Microsoft Points.
I think this is what it is going to look like. Hopefully they will figure out a way to deal with the people who go all in all the time. It looks pretty though and since it's going to be free I'm definitely picking it up!

pic from teamxbox site.
UPDATE: NO LONGER FREE (CheapyD edit)
http://www.joystiq.com/2006/07/20/joystiq-interviews-greg-canessa-of-xbla/
Besides Lumines Live!, one of the other games people are looking forward to is Texas Hold 'Em poker. Talk about what's in store for that.
First of all, it won't be free. We haven't decided on what the final price will be, but it will not be free. As far as incentives, we want to make sure gamers play with a purpose with a game like this that doesn't have any actual risk/reward. We will have a persistent bankroll system tied to your gamertag that will allow those who have built up enough money to enter higher-quality tournaments. Then, if you run out of money, you have to enter the freebie tournaments to build your bankroll back up.