I feel a little like Paul Revere. The casinos are open! The casinos are open! I’m guessing they are coming by both land and air.
From all accounts that I could read, the vast majority of Las Vegas fans have been overjoyed to return to the casino floor. The changes that we have talked about over the past few weeks have not deterred many. I personally have yet to venture in myself to see if it appears that anyone has been taking my advice on altering strategy for the face-up games.
I remember that when Ultimate Texas Hold’em Poker was first introduced many years ago, there was a gambling message board where one vocal reader was sure that UTH would fail because players would share their pocket cards with the rest of the players and this would generate such an advantage as to make all the casinos rip out the tables.
There was even one gaming jurisdiction that initially would not approve the game because they claimed that they had proved that the game could be beat with collusion. I asked how they had proved it and they said that they had run every possible hand with 6 players and perfect strategy. I don’t think I had ever laughed so hard. They were claiming they had run roughly 14 sextillion hands — that’s a 14 with 21 zeros after it. It’s simply not happening.
But, of course, this prompted questions about the power of collusion for a game like Ultimate. And now, it is no longer collusion. The cards are dealt face up for all players so everyone can see. Back then, I had done some work on the impact of this and found it to be incredibly small. Reading work done by others more recently, they seemed to concur.
Why would this be?
In order for information to be valuable, it must be actionable. That is, a player must be able to do something different than he normally would without this information. The fact that the information changes the probability of the player winning, by itself, is not actionable.
For example, if a player is dealt pocket Aces with cards being dealt face down, we know that the player will win this hand almost 85 percent of the time and he should obviously make the 4x wager. Does this win frequency change if he sees that one of the remaining Aces is dealt to another player? Absolutely. It will decrease even further if both Aces are dealt to other players.
But, even in this case, the hand would still warrant being played at 4x. Nothing actually changes. The fact that he might win the hand only 57 percent of the time does not change his strategy at all. Only if the win frequency were to drop to below about 55 percent should he potentially hold on the 4x wager.
Are there circumstances in which this will happen? Yes. But that brings me to the second part of the equation. he frequency that the circumstance actually happens.
Being dealt any particular pocket hand in Texas Hold’em varies from 0.3 percent for suited hands to 0.45 percent for pairs to 0.9 percent for unsuited non-pair hands. So, no particular hand is all that common.
Then the trigger also needs to happen. So, how often will the player have a pair and both of the matching cards are dealt amongst the four other cards dealt to players? Roughly speaking, about the same probability that the player has the pair in the first place. So the overall probability of the event occurring is roughly 1 in 45,000.
And for a pair of Aces, it doesn’t even change the strategy. For a pair of 3’s or 4’s it probably does. So, perhaps 1 in 1,000 hands overall, we will change our strategy and eke out a couple of percentage point difference in expected value — but that 2 or 3 percent has to be multiplied by the 0.001 (1 in 1000) to get the true impact.
We then have to factor in that the very complex strategy for UTH has been complicated even further, meaning we have to hope that human error doesn’t make up for any benefits that the player might get.
The bottom line is that UTH is not a game that you can expect to derive much advantage at if it dealt face up — especially with only three players at the table.