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# An Introduction to Texas Hold'em Bonus Poker

24 March 2006

Progressive Gaming announced this past week that their hot new table game Texas Hold'em Bonus Poker (THBP) has been approved in Nevada. The game has already been playing in numerous jurisdictions with much success, and adding the game to the Nevada scene should only give it that much more exposure. While I didn't work on THBP for Progressive, I did do the math behind Shuffle Master's Ultimate Texas Hold'em (UTH) that is just coming out of the gate. While the games are different in a number of ways, the math required to analyze these games is very similar and very complex.

Games against a Dealer are always more complex than 'paytable' games because of the number of cards dealt. Games with community cards against the Dealer can make you want to pull your hair out! When the cards belong solely to the Player, it's very easy to quantify the hand and come up with a strategy. When 3 to 5 of the cards also belong to the Dealer, the trick is coming up with a way to categorize the hand, taking into account the strength of the community cards. It's not enough to tell a Player to Raise if he has Three of a Kind. The Three of a Kind may be the three community cards. If the Player's cards are Ace/King, that's great. If they are a 2-3, then he's an almost sure loser. Doing all this analysis for UTH took me several weeks, so I've not yet had the time to complete my analysis of THBP. This article is meant as an introduction to the strategy to the game, and hopefully, in coming weeks, I will have the time to complete the strategy and report back.

First, let's cover how the game is played. Each Player makes an Ante bet and receives his two pocket cards. After looking at his cards, the Player has to make a decision to Fold, surrendering his original wager, or to make the 'Flop' bet, which must be twice the size of the Ante bet. Since all other wagers in the game are optional, the strategy at this point is based on whether the Player will win more (or lose less) by surrendering the 1 unit or by risking 2 additional units. To answer this, we also must realize the payout structure. If the Player beats the Dealer, he will win even money on his Flop bet. His Ante will push, unless the Player beats the Dealer AND has at least a Straight (in some jurisdictions, a Flush) or better, at which point, the Player will get even money for his Ante wager as well.

I used a computer simulation to provide me with the results for this very important strategy decision. Basically, I simulated each of the possible pocket hands against a 'random hand'. Unlike real table poker, the Dealer is as likely to have an unsuited 2-7 (worst possible starting hand) as he is an A-K. When you play table poker, you can be reasonably certain that the lesser hands are folded early, but that's not the case here. The Dealer is in until the very end regardless of his hand. As it turns out, the Player is only supposed to fold about 11% of the time (in the Straight version). The only hands that warrant a fold are suited 2-3 and 2-4, off suited 2-3 thru 2-8 and off suited 3-4 thru 3-8. In the Flush version, we add a handful of hands to the Fold list (off suited 2-9, 4-5 and 4-6).

From what I've seen and heard, the Players who have jumped into this game without any strategy have generally folded TOO often. Hands that should be quickly discarded in regular Texas Hold'em, have quite a bit of value in this game. Even if they are net losers in the long run, the Player will still lose less by not Folding.

If a Player follows the strategy I've shown below and chooses to decline the other optional bets (which I'll get to in a moment), he will find his payback to be a mere 86.45%. The final 2 optional bets are bets that should be made ONLY when the game has a positive expectation for the Player (he will win more often than he will lose), and this is how the Player brings the overall payback back to something a bit more palatable.

To continue with the description of the game, once the Players have decided to make the Flop bet or Fold, the Dealer turns over the first 3 community cards (the Flop). Each Player can now make an additional wager equal to his Ante, if he chooses, called the 'Turn' bet. The Dealer will then turn over the 4th community card (the Turn) and again, the Player will have the option to make another wager equal to his Ante if he chooses, called the 'River' bet. Both of these wagers will pay even money if the Player beats the Dealer.

Unfortunately, this is where the strategy gets VERY complex. Given the incredible number of combinations of partial hands and relative ranks of cards, it is very difficult to put together a strategy that can be used by even an expert player. So, the goal has to be to come up with at least some guidelines, with the understanding that there still may be some hand we are playing wrong, but the impact of this is minimal. So, for now, I'm going to cover some of the basics of the 1st optional wager. Hopefully, I will complete my analysis soon and will be able to give you further information in the coming weeks.

For now, I will list a partial strategy for the Turn bet:

• If you have a Straight or better after the Flop, make the Turn bet.
• If you have a Three of a Kind which includes one of your pocket cards, make the Turn bet.
• If the Flop is a Three of a Kind and your hand is a pocket pair or a Q-6 or better, make the Turn bet.
• If you have a Two Pair, EXCEPT where you have pocket 2's, make the Turn bet.
• If you have the High Pair on the table (either with pocket pairs or by pairing up against the high card), make the Turn bet.
• If you have paired up against the low-card on the table, bet the Turn bet IF the Flop does not make a 3-Card Straight or a 3-Card Flush unless when combined with your other pocked card, you have a 4-Card Straight or 4-Card Flush.
• If you have paired up against the middle card on the table, bet the Turn bet UNLESS the Flop makes a 3-Card Straight Flush (or 3-Card Inside Straight Flush) and when combined with your other pocket card does NOT make a 4-Card Straight or 4-Card Flush.
• If you have a pocket pair greater than the low-card on the Flop, and the Flop does not contain a Pair or Better, make the Turn bet.

The strategy shown is not meant to be comprehensive at this point, but if you're going to play without a complete strategy, you might as well have at least a partial strategy. Like all table games, there is no bluffing and hunches involved. There is no point in reading the Dealer's face to try and figure out if he can beat your Pair or not. It's all about the math. I have not seen a published payback from Progressive yet, and the word on the street says the payback on this game is weak. So far, my own analysis shows that the word may be incorrect. However, to earn the full payback will require learning the proper strategy. If anyone has any questions about this or any other game, I can always be reached at elliot@vpheaven.com.

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Elliot Frome

Elliot Frome is a 2nd generation gaming author and analyst. His father, Lenny Frome was considered one of the premier authors of Video Poker books. Titles include, Expert Video Poker for Las Vegas and Winning Strategies for Video Poker, which includes the strategy tables for 61 of the country’s most popular versions of Video Poker. Check out Compu-Flyers website at www.vpheaven.com, or drop Elliot an e-mail at compuflyers@prodigy.net.

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Elliot Frome
Elliot Frome is a 2nd generation gaming author and analyst. His father, Lenny Frome was considered one of the premier authors of Video Poker books. Titles include, Expert Video Poker for Las Vegas and Winning Strategies for Video Poker, which includes the strategy tables for 61 of the country’s most popular versions of Video Poker. Check out Compu-Flyers website at www.vpheaven.com, or drop Elliot an e-mail at compuflyers@prodigy.net.

www.vpheaven.com