Last week I discussed the importance of net win vs. expected value when looking at wagers of different sizes. The term expected value was originally used mostly to describe video poker hands. Since the wager size is the same from hand to hand and the payouts are all essentially odds based - meaning they pay a certain amount for each unit wagered as opposed to a fixed dollar amount, using the expected value works fine. But, in a game like blackjack where the Player has the option to double down, we need to look at net win (or loss) and not expected value. We lower our win frequency (which lowers the expected value) when we double down, but we still do so because in the end we win more money, which is the real goal.
I'm not sure any game makes this as apparent as Ultimate Texas Hold'em with its most unique betting structure. Roger Snow and I were on our 20-something version of the game when we decided to go with a betting structure similar to the one that eventually got used. The idea was that you could bet ONLY once, but the earlier you bet, the more you could bet. Take more risk, get more reward!
For those not familiar with how Ultimate Texas Hold'em works, here's a quick recap. The Player makes two equal wagers - an Ante and a Blind. He then receives two cards face down. The Dealer also gets two cards face down. There will eventually be five additional community cards - as in Texas Hold'em. But for now, the only information you have is your two pocket cards. At this point, you may make a wager equal to 4x your Ante wager or you may check. If you bet at this point, you're done betting. The dealer will then reveal three of the community cards. If you have not bet yet, you may now bet 2x your Ante wager or check. The Dealer will now reveal the final two community cards, which allows you to see your complete hand. Now, if you have not wagered before, you may bet 1x your Ante wager or FOLD. The Dealer will reveal his two cards and resolve the wagers. The Play wagers are always in action. If the Player beats the Dealer, he gets paid even money. If he loses to the Dealer, he loses his Play wager.
I can't think of another game that uses this type of betting structure or anything like it. Most games are a series of Play/Fold or Play/Check bets. Ultimate Texas Hold'em uses a bet early, bet more approach. To understand the impact of this subtle difference, we just need to look at the strategy decision making process. Normally when faced with a Play/Check decision as the Player is after receiving his two cards, the decision is based on whether or not the Player is more or less likely to win. If he is going to win more often than he loses, he makes this wager. In Texas Hold'em Bonus Poker, the latter wagers are of this type. They are 'optional' wagers meaning the Player may make them or check. In this case, the Player makes the wager when he is favored to win the hand. It doesn't matter what he did before or what he will do next.
However, in Ultimate Texas Hold'em, the decision is a bit different. By betting 4x, the Player loses the ability to wait and bet 2x or wait longer and bet 1x (or even Fold). Like in our blackjack scenario, the Player is giving up something by making the wager early. He is giving up the opportunity to bet later with more information. If Ultimate used a betting structure of get two cards, bet 4x or check, flip three community cards, bet 2x or check (regardless of whether you made the 4x wager), etc... the strategy would be vastly different. In this case the Player would actually make the 4x wager a full 50% of the time because the Dealer has no advantage over the Player in terms of who will win the hand. Both get seven cards with two being pocket cards and five being community cards. But, because the Player has to give up something to bet 4x, we find that the strategy actually dictates to 'wait and see' when the hands are very close to the midpoint. Thus, if the Player is going to win 52% of the hands based on his first two cards, it might pay for him to wait to see the three community cards and then if this work out, bet 2x and if they don't wait for the final cards.
If the Player were to never bet 4x or 2x, his 1x wager would have a very high expected value. After all, he would Fold when his hand was weak and Play when it was strong resulting in a lot of wins for the Play wager. But the Wager is only 1 unit. He needs to win far fewer 4x Play wagers to achieve the same net win. If a Player faces a 1x situation 1 million times with a 1.2 expected value, he will win 200,000 units. If he faces a 4x situation 1 million times with a 1.08 expected value, he will win 320,000 units. So, it pays to take greater risk in search of greater reward - up to a point.
It is worth noting that the general consensus is that Players do not make the 4x wager often enough to maximize their payback. Most likely because making a 4x wager and having lady luck frown on you can wipe out your bankroll rather quickly. The game was specifically designed in this manner. While betting 4x, the Player will win fewer hands than when betting 1x (if you ignore the opportunity to bet 4x and 2x). Thus, the Player may feel better by winning more hands, he's just not winning more money!