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Expected Utility, Part 2

In Expected Utility, Part 1, we explained how one's utility is not necessarily equal to the expected value of the hand. Most of the time, people should play as risk-neutral, meaning that their expected utility is equal to expected value. However, there are times when people should be risk-averse, meaning their expected utility is lower than their expected value. For instance, most people would not bet their whole bankroll on a 51-49 shot. While this is a slightly +EV move, the utility a person gets from doubling their bankroll is likely much smaller than the utility they stand to lose from blowing their whole bankroll.

There are times when people might even be risk-averse with their chips at their table. Most of the time, this is an incorrect play, but there are times when this is warranted. For instance, many tournament players are risk-averse with their chips. This is because you are not guaranteed to win anything if you double up in a tournament. However, you are guaranteed to be out of the tournament if you lose your entire stack. (It should be noted that a lot of players are overly risk-averse in tournament situations to the point that it is heavily -EU).

Nevertheless, there are some instances when it might even be in a player's interest to be risk-loving with their chips at the table. This means that an -EV move might actually be a +EU move. There are not many instances where this is the case, but it can occur.

An -EV move that is +EU means that the action is definitely -EV for the individual hand, but it may turn out to be +EV in the long run assuming certain other factors come into play. Basically, the move is a mistake if you just consider the one pot alone. However, when factoring in later pots or later play in the tournament, the move may turn out to be +EV.

Before proceeding further into this article, it needs to be made clear that this type of move is for expert players only. Do not attempt to employ these theories if you are an average or even above-average player. Generally, only professional-level players are able to profitably apply these theories.

Opportunity Cost (Tournaments)
If you are playing an online poker tournament, you can likely multi-table a cash game or two on the side as well. Some players only like to play one game at a time, but most internet experts are comfortable with multi-tabling.

However, in a live casino game, multi-tabling is either extremely difficult or impossible. You will almost certainly miss out on hands in the tournament, which will certainly decrease your EV from the tournament. If you attempt to multi-table, most people get extremely angry with you because you end up slowing down the game considerably. Because of this, some poker rooms will simply not allow it.

Thus, when you are playing a tournament at a live casino, you are giving up the opportunity to play in a cash game. When deciding whether to play in a tournament, you would need to consider the hourly rate you expect to make from the tournament versus the hourly rate from the cash games at the casino.

If there happens to be very juicy cash games that night or your hourly rate from cash games are just really high in general, an extra aggressive style of play at a tournament might make sense. It may be profitable to be risk-loving in the tournament (hence certain -EV situations turn out to be +EU).This is because you will quickly be in position to win the tournament (hence the expected value of continuing to play in the tournament would be really high), or you would be able to play in the cash games.

Simply holding on to a puny stack might be the lowest EU of all situations. Mathematically speaking, it may make more sense to just give up on your stack on go play in a cash games because your expected hourly rate is higher in the cash game than holding onto that stack.

The reality of the situation is that people are not solely concerned with their hourly rate when playing poker. Many want to play in tournaments just for the enjoyment factor of the tournament. It is also very difficult to know for sure what one's expected hourly rate of a tournament is compared to the cash games at a casino.

This sort of opportunity cost situation does not apply as much to online players because playing a tournament just means one extra window on their computer screen. Sure, people generally max out on the number of tables they can play at once. Nevertheless, playing in a tournament is generally less intensive than playing in a cash game because you tend to fold more preflop. Thus, it really does not affect your ability to play cash games nearly as much as a live tournament does.

Bullying (Tournaments)
Some players only play well when they possess a lot of chips. This is because they frequently try to bluff people out of the pot and make other aggressive moves. They also want to be in a position to capture anyone's entire stack in one hand. These sorts of players most often aim to win the entire tournament. Their focus is not so much on survival as capturing first place.

Sometimes, this sort of play makes logical sense. In tournaments that are winner-take-all or heavily top-weighted, one should certainly go for the gold. For aggressive players in these sorts of tournaments, an ultra-aggressive strategy may pay off. These sorts of players would attempt to build their stack up as quickly as possible, even if it means they make some slightly -EV decisions for the chance of doubling their stack up.

By gambling it up, these players hope to build a powerful stack that will let them bully their opponents into submission. For these players, the -EV decisions they make at first turn out to be +EV over the long run because they play so much better with a larger stack.

Big Fish (Cash Games)
Sometimes, a poorly-skilled player will have a huge stack in a no-limit cash game. This person may have just bought in for a lot more money than most people, or this player may have just had a huge winning streak.

In a no-limit game, this player is apt to lose this entire stack in a hand or two, given the right conditions. When a fish with a huge stack is in a game with several good players, all of these players are gunning to get their stacks large enough to be able to take out the fish in one hand. Not only does the fish have a lot of money to lose, this type of player is not used to playing a large stack. Playing an extra-large stack requires different strategy than playing a small or mid-sized stack, and many casual players are ill-prepared to play such a large stack.

Some brick-and-mortar casinos allow a player to buy in for as much as he or she wants. So in these cases, a professional player could just buy in for as much as the big fish has, hoping to double up. However, all internet poker rooms and a lot of B&M casinos have limits on how much people buy in for. This means that in order to double up through the fish, one would have to increase his or her stack a lot by winning chips.

For instance, suppose you are in a $5-$10 no-limit hold'em game. The max initial buy-in is $1,000. You have $1,000 in chips, player A has $500, player B has $1,000, player C has $2,500, player D has $3,000, and Player E has $3,000. Player D and E are huge fish, while players B and C are about average.

In this case, even if you hold a monster hand against Player D or E, you can only get about 1/3 of their chips. In contrast, Player C could potentially get 5/6 of Player D or E's chips, a much heftier sum.

Against a big fish, one can potentially have huge edges. This is because inexperienced players will frequently pay off a player who clearly has the nuts. Thus, if you are able to build a huge stack, there is the chance that you will be in a situation where you are both all-in where you are a lock or at least a huge favorite.

It is likely once Player D or E loses their chips, they won't be back for awhile, at least not with that type of stack. Thus, there is a certain sense of urgency to get a larger stack in order to bust out the fish before others do.

However, getting that large stack is not always easy. One would have to win quite a few hands to get the type of stack needed. In this case, it may pay off in the long run to be fairly risky with your stack. Loosen up and see more flops. If you are making a decision for all your chips and are somewhat unsure of what move to make, it may be better to just go ahead and push because the rewards from having a huge stack in this game might be really high.

Of course, this does not mean you should be foolish with his stack and go all-in when you are a significant underdog. However, in cases where it's probably close to 50-50, it may be beneficial for one to lean towards gambling it up instead of avoiding a confrontation. Knowing when a situation is around a 50-50 is very difficult for poker players, which is why this move should only be done by expert players (expert players are also more likely to be able to bust a fish once they have a huge stack, too).

Inducing Tilt (Cash Games)
A lot of players in no-limit games can play very well, except when they go on tilt. When this occurs, these players will frequently drop a lot of money at the table. Many of the higher-stakes no-limit games are virtually unbeatable unless a player at the table goes on tilt. Most people should just avoid games this difficult, but many play in them anyway.

Nevertheless, once a player or two goes on tilt, profit opportunities may arise. This means that in these sorts of games, making plays to induce a player to tilt may pay off in the long run.

For example, certain types of bad beats may tend to destabilize a player. When on tilt, this player may tend to play "revenge poker" against the person who bad beat him or may just play bad in general. This is a heavy +EV result for the person who set the player on tilt.

So in these types of games, it may make sense for a person to make a -EV move if the person thinks there is a good chance that it may set another player on tilt. An example would be calling a large bet with a draw. Some players get extremely upset when others draw out on them, so calling and hitting a draw may set them on tilt.

Again, this sort of move should be used with extreme caution. For it to work, a player needs to get lucky enough to win the hand, the other player needs to go on tilt, the other player needs to not leave the table, and the other player needs to lose money to you while he or she is on tilt. These are a lot of "ifs," which means that even an expert should be wary of making even a modest sized -EV move in an attempt to set an opponent on tilt.

Advertising (Cash Games)
Many beginners' poker books talk about the "advertising" value of the bluff. This means you should show a bluff or try to get caught bluffing so your opponents will be more likely to pay you off later when you hold a hand.

Most books advise against this practice, with good reason. Most people play in poker games where players do not really pay attention to each other. This is especially the case with internet poker games. This means that people will not pay attention to your advertisement, so you just end up wasting money. A lot of players also have heard of this move and will not be fooled by your deceptive play.

However, there are a few cases when "advertising" may make sense. For example, suppose it turns out that someone new will be joining your buddies' weekly home game indefinitely. This player does not know how to play, and you happen to be a very tight, straightforward player.

It may pay off to try to bluff out this player at first, so his first impression of you is that you are a maniac. First impressions are very important in poker, just as they are in life. This player may continue to play you as a maniac in later sessions, even when it should be abundantly clear to him that you are a tight, straightforward player.

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