Mobility
From The Othello Wiki Book Project
Definition
Mobility is a general measure of the number of moves a player has. Usually expressed as 'High' if there are a lot of moves available or 'Low' if there are few moves available.
A player's Mobility either increases or decreases and, when dramatically low, could leave nothing left but suicidal moves.
If white had 2 more moves his mobility has increased ; you would not say he has 2 more mobility.
Average mobility during the midgame is around 10 possible moves that players have to choose from. Assuming that both players are experienced.
George Ortiz wrote for the Australian Federations (http://www.othello.asn.au/) newsletter, OZthello in 1996.
"The opening phase of Othello can be described as a "battle for mobility" often referred to as mobility optimization. Each player tries at each turn to have greater mobility (more moves) than the opponent. To do so, one must ideally try to increase his own mobility while decreasing the opponent’s mobility. If one player can manage to reduce the opponent's mobility to zero (or near zero) then that player will be able to "force" his opponent into making undesirable moves and follow through with an easy win. In any case, greater mobility in the mid-game most often translates to a winning position in the endgame. But how can this theoretical concept be applied in practice?
One technique which is very powerful is the evaporation technique. This technique consists of trying to force your opponent to flip as many of your discs as possible, in an attempt to quickly run him out of safe moves (while making sure you’re not under the risk of being wiped-out!). To successfully force the "evaporation" you should always play in areas in which your opponent already has access while keeping your discs in a connected cluster (a method sometimes referred to as "curling into a ball"). While this technique can provide dramatic results it is very unlikely you will be able to apply it unless you are playing a beginner. Indeed this technique requires a fair amount of "cooperation" from your opponent making many "bad" moves which flip lots of frontier discs. To describe the slightly more standard technique of mobility optimization we need to define a key concept in opening strategy, the quiet move.
Because of the nature of the rules of Othello, most moves you make tend to increase your opponent's mobility and decrease your own (there are suddenly more discs for your opponent to flip and less for yourself). However there is one type of move which doesn't follow this trend: the quiet move.
When there are no "outstanding" moves to make players will want to play a quiet move to maintain their mobility (neither increase it, or decrease it). This means that it is a good idea to always have quiet moves in reserve. Therefore players should always try to "set-up" new quiet moves in the opening phase and by the same principle try to reduce the opponent's quiet moves."
I have often heard it said that while white has a parity advantage towards the end game, black begins the game with a mobility advantage. That is, it is considered by some that it is easier to restrict the number of moves that your opponent has to choose from in the early stages of the game when playing black.
This is why, i believe that Othello is played on a board with an even number of spaces on the edge, 8x8 (standard) and 10x10 Othello (variant) and not a 9x9 (for example) board. On a 9x9 board because of the odd number of squares, black would not only have a mobility advantage but also a parity advantage.
I would like to take the time to try an put down some thoughts on mobility. Not why mobility is important! Ive already had George explain that for me. But instead how a player can go about the basics of considering mobility as an element of strategy involved in Othello.
This is meant to be quite a simplistic guide and is i hope quite chatty in the way it is written. Hence it should be reasonably easy to read.
If you have any queries about what ive written please leave me a comment in theTalk section of my profile.
If you think you can improve on anything, be it my Grammar or theory, Please feel free to update.
Thanks, David.
| Table of contents |
Restricting Mobility in the opening
One basic way to restrict the mobility of your opponent is to establish a simple or quiet move that will be open to your oppoenent on his/her next turn and simply to remove this possibility with your move. This can be shown when considering some of the typical book openings (see Opening Book) moves that are regularly played by stonger players.
Consider the position shown in Figure 1.0
Figure 1.0
Image taken from Wzebra 4.2.2
Figure 1.0 shows the position obtained from the Tiger opening (c4,e3,f5,e6,f6,c5) after move 6.
The typical replies that are played by black from this position are:
- Stephenson (C3)
- Leaders Tiger (D3)
- Tiger (F4)
- Brightwell (D6)
All of which have one primary aim; to remove the threat of white playing D6 on its next move. By either removing whites stone at D4 or in the case of Brightwell, taking the D6 move itself. these are shown below.
Images taken from Wzebra 4.2.2
These openings however yield differing results in terms of mobility.
| Opening after 7 moves | Whites Number of Moves | Blacks Number of Moves |
|---|---|---|
| Stephenson | 7 | 12 |
| Leaders tiger | 5 | 10 |
| Tiger | 5 | 10 |
| Brightwell | 8 | 8 |
If it is desirable to increase the margin between the number of moves you have and the number of moves your opponent has, then in this scenario, it would seem that Brighwell is inferior and that there is little difference between the other 3. however these are only the values for mobility at one stage of the game. othello is dynamic, mobility will alter from move to move. it is therefore inaccurate to to assume a move is correct solely on the basis of a short term gain in mobility. Mobility as i understand it is a long term goal, where you tend toward a position that forces your opponent to make sacrifices.
Restricting mobility on more than one line
It is possible in some cases to restrict the mobility of your opponent by removing more than one of his/her potential 'good' next moves. For example, the continuation of the Tiger (c4,e3,f6,e6,f5,c5,f4,g5,g6,f3) leads to the position shown in Figure 2.0
Figure 2.0 + 2.1
Images taken from Wzebra 4.2.2
White is threatening two easy moves at D3 and G4. Although perhaps unnoticable at first to someone that is not familiar with the position, Black has in fact the ability to remove both of these moves by playing F7. if Black had focused on removing only one of these moves then white would have been left in a position to take advantage of the other.
Forcing your opponent to restrict his/her own mobility
Figures 3.0 to 3.2 demonstrate how it is possible to force your opponent to reduce their own mobility. By threatening the corner with a move to E8. In this position white has two options: suffer the loss of the a8 corner, or play F8 but sacrifice mobility. This is because the white stone at F2 is severly poisoning (see poison) whites move to F8, forcing white to create a wall.
Figure 3.0, 3.1 + 3.2
Example taken from Reversi - An Animated Guide (http://samsoft.org.uk/reversi/) by Steve MacGuire
Images taken from Wzebra 4.2.2
Preserving your mobility
As George explained (above) the easiest way to preserve your mobility is to opt for a quiet move, at the same time, this should also entail restricting your opponents mobility. As finding a quiet move will not give away any additional moves to your opponent as well as not disturbing other moves that you may have in other regions. See Quiet move for examples.
However in some circumstances it is desirable to make Loud moves to gain access to other key areas of the board. This also has implications when trying to restrict your opponents mobility.
An example of this is one of my favourite openings at time of writing, (and im probably being silly posting this because so many people ignore the correct lines -- but hey, were here to educate)
Im not too sure of the appropriate name for the opening either (prehaps someone can help me out here!!) Ive sometimes heard it referred to as 'Berg' but im yet to find any source online or other that confirms this.
Not wanting to go into the exact specifics of the opening, let's concerntrate on the position obtained after move 11 (c4,e3,f6,e6,f5,g4,g5,c5,c3,c6,d6). Figure 4.0 shows this position, black has just played d6, limiting the choices that white has. Six moves to blacks 12 to be exact. And of the moves that white has, none of them seem to be quiet.
So how do we determine where the most appropriate move is?
Firstly lets consider one of the principles explained above, restricting your opponents mobility, try to determine where your opponent might want to play if they were considering this exact same position for there move. In this instance Black would most likely like the look of a move to D3. it neither gives white to many extra options and keeps black central amongst whites pieces.
So consider removing this move for black. White can immediatly rule out taking the move itself, as it has no access. Leaving only G6 and H1 as options. G6 should clearly be a poor choice creating a wall and restricting whites mobility in the south. H1 on the other hand, although a loud move acctually does three things:
- It increases whites mobility from 6 to 11
- It achives the goal of removing blacks D3 move
- In addition gives white access to D3.
This is shown in Figure 4.1. Three for the price of one. That kind of offer only comes round in supermarkets once every blue moon.
Figure 4.0 + 4.1
Images taken from Wzebra 4.2.2
Therefore, Loud moves can not be ignored as a potential for increasing mobility. Infact many new players once past the maximisation as a strategy phase, end up in a new phase that see's them go for the smallest move they can without considering mobility, shape or position. this leaves them vunerable to being run out of moves in the midgame.
Holding edges in the mid game and mobility
During the mid game holding edges can make it extremely hard to maintain decent mobility. This is because moves that you make are likely to flip stones in multiple directions, the more edges you hold, the louder your moves are likely to be. This is an aspect that i picked up on when i was first learning to play othello and when playing opponents of a similar level i often ended up in positions similar to Figure 5.0
Figure 5.0
The only moves being played were in the centre (minus the x squares) and no pieces being played on the edges until i was forced to.
Not to say this is a correct strategy, infact it is probably completely wrong. Although if you can encourage your opponent to take many edge pieces early on you are likely to be able to force your opponent to make loud moves in the midgame. However you are vunerable to a technique known as 'edge grabbing' (see below) and hence running the risk of being run out of moves yourself.
Most well played games that i have observed see both players holding their fair share of edges. obtained from a combination of edge grabbing and egde avoidance.
Other methods for restricting your opponents mobility
Checkerboarding
See Checkerboarding
Edge grabbing
See Edge grabbing
More advanced theory
Should be discussed:
- In Timing
- In Tempo
- By someone other than me
(work in progress)
