Utility Odds

As promised, today I want to talk about the concept of "utility odds", as described by Arnold Snyder in his excellent poker book sequel The Poker Tournament Formula II. In a nutshell, Snyder argues that it is utility odds, and not just normal pot odds or implied odds, that are the most important mathematical determinant in making call-or-fold decisions in poker tournaments. I mention this point because, frankly, I think Snyder is clearly quite on-point with his whole discussion of chip utility and his focus on this concept throughout his writings, but I find this particular concept of utility odds to be the hardest to quantify of the various aspects of the ramifications of chip utility that he explores.

Snyder's basic point regarding utility odds can be summed up well with an example he uses in the book. Snyder gives an example of a well-known poker pro who called allin with just a naked flush draw during the first hour of one of the smaller World Series of Poker events a year or two ago. I don't remember who it was and obviously it doesn't really matter, but all you need to know is that the guy was an accomplished tournament poker professional, he was at about 80% of the starting stack in the event somewhere during the very first blind level, and there he went calling an allin raise on the flop with just a flush draw, in a situation where he was only getting close to even money to make such a call. Snyder explains that many spectators were in disbelief that a pro would make such a call, and yet Snyder explains that he too would have made the call in a heartbeat.

The key to how a skilled tournament player can call off his stack at around even money pot odds with just a 35% chance flush draw lies in the relative value -- the chip utility -- that the skilled player can obtain by amassing the stack he would get if he manages to double up on this hand. At 80% of the starting stack, and this being one of the smaller (faster) WSOP events, this player was already sitting with only somewhere between decent and competitive chip utility, and a good half of the 100 big blinds level that Snyder considers full utility. So the thinking is, this guy is already in pretty bad shape, and he needs to get himself back to full utility as quickly as possible, or he knows he is more or less hopeless to make any real noise in this tournament. And, he also knows that if he can get up to full utility and get himself a larger chip stack than most of the players at his table in the process early on in the tournament, then he will be able to make great use of those chips to get himself more and more chips as he can open up his arsenal of poker weapons to include all the types of moves I discussed in my posts from late last week. So to this player, being that he is skilled compared to most other entrants in this event, the value to him of getting back from his weak chip position up to full utility early here, and the relative value of him doing that as opposed to one of the other weak-tigher players doing so, gives him the ability to make a call at less than the "required" pot odds. This is because if he wins, it significantly enhances his ability to grow his chip stack, and eventually to cash and score big in the tournament. In other words, the truly skilled tournament player can call allin with a flush draw early getting only close to even money, because if he loses the hand, he was already in a fairly desperate situation anyways and he hasn't really lost much, and if he wins that hand, he will suddenly be at full chip utility and in a situation where he can really do some damage in the tournament. It is all that extra damage the professional player will be able to if he is able to win that pot and get himself up to full utility do that enables him to take the worst of it from a pure pot odds perspective early in a large mtt.

That, in a nutshell, is the concept of utility odds. As far as my reaction to this idea, in general I have to say once again that Snyder is on to something. I mean, I ask you again to think about the times you might have sat on the rail and watched one of the better mtt players playing in a poker tournament. I know personally I have done this many times and have remarked to myself how these better mtt players do not mind taking chances early to either double up or get busted. Look at the Lindgren's and the Gus Hansen's of the world -- they play their tournaments the same way. This is because they know it is worth taking some chances, maybe even taking on a race very early in a tournament under the right circumstances, to either try to get themselves up to full (or better) chip utility, or to bust out early trying. That's what it comes down to in the end -- especially in the world of online tournaments which are basically all faster than their live counterparts -- you just have to double up early and it's ok to bust out early and move on to something else if that's what it takes. I know there is definitely an element of that to the way I play in mtts, and I have personally witnessed the same strategy from most of the other tournaments I have watched from players whose mtt skills I respect as well. I might easily call an allin preflop very early in, say, the nightly 28k guaranteed on full tilt, with my AK, even when it is obvious from the action that my opponent is holding a pocket pair of some kind, making me a slight dog in a situation where I still have a fair number of big blinds in the tournament to fold and wait for a better spot if I so choose. Although again, I've never thought of this in terms of "utility odds" per se, the idea here is definitely that I want to take a shot at getting a big stack early, or go home trying, because I know with that big stack early I can significantly increase my chances of growing an even bigger stack and eventually cashing and making a final table run. This is exactly what Snyder is getting at when he talks about using utility odds instead of pure pot odds in tournament decisions.

The one complaint I have about this whole thing is how hard it is to quantify something like utility odds. I mean, fine I accept that a truly skilled mtt player and someone who knows how to use a big stack like a weapon to crush the other players at his table has the freedom to make some calls that might not be exactly right from a pure pot odds perspective just because of the added value he gets if he does in fact win the hand and get himself that big stack. But surely this idea does not mean that a skilled player can call off his stack drawing at just an inside straight draw with one card to come, just because if he does manage to hit his 11-to-1 shot on the river he will then achieve full utility. So the question that Snyder does not really address -- and I can't really complain because I'm quite sure there is no good bright-line answer to this -- is a way to accurately quantify utility odds. In the end I suppose this calculation, if one can even be accurately devised for such a number -- is going to depend on exactly how close to full utility one's stack is before the hand in question, just how many big blinds one will be left with if he wins the hand in question, and most of all, just how much his chances of a big score in that tournament will increase if he is able to obtain such full utility early on in the tournament like this. All of these variables will need to be taken into account, in combination of course with the actual pot odds involved in the hand in question, in order to come up with some sort of actual calculation of utility odds in any given situation. And those numbers will be really different for every individual player (depending on their current mindset, how well they play a big stack, etc.) and in every different tournament situation, but from my perspective at least those are the types of things that I will try to consider as I face such decisions at key points in poker tournaments going forward. I also think Snyder's approach fails to consider the likelihood of a strong player being able to wait for a better spot to double up to full utility with better pure math chances of doing so, something which I'm sure Snyder would not deny, but that doesn't change the fact that utility odds are a useful way of looking at poker decisions in tournaments that simply do not exist at all in a cash game or a "pure poker" context.

There is so much more to be said about Arnold Snyder's thoughts when it comes to poker tournaments, and you can see more about that here later this week as I continue to read deeper into his second book and continue to think in new ways about my own poker experience.

For now, just revel in the Eagles' 38-3 domination of the Rams, easily the worst defense in football, to start off the 2008 season the same way almost every season starts off lately for everyone's favorite Philadelphia sports team, and maybe I'll run into you this week at the tables.