Backgammon strategy applied to SCRABBLE(tm)
So Stewart's recent ADEIRSS opening rack has focused my remaining brain cells on the ploy of the deliberate phoney.
Publicly, experts would have you believe that playing a phoney is always wrong. They would pretend that the deliberate phoney is so rarely useful that it is hardly worth considering.
Secretly, the experts know that if everyone was well-versed in the nuances of this ploy, it would be even less useful. I reckon that's the real reason it's not covered in detail in The SCRABBLE(tm) Player's Handbook
Of course I'm 99% kidding - and the reality is that a deliberate phoney is only a "technically correct" play when a few unlikely events coincide:
1. PASS looks like it might be better than any other move
2. By passing, you would allow your opponent to make a valuable inference, i.e. - she'd know exactly what you're up to.
3. You can think of a phoney which has good enough score+leave that if left unchallenged, it would be better for you than passing.
4. The information you'd give away by phoneying [and showing those tiles] is no more costly than the information you'd give away by passing.
When you do play a deliberate phoney, you are offering a binary choice to your opponent. They can accept it or reject it. If we assume that they'll always make the right choice, then we must only offer them the choice if we know that either response will still benefit us. However, if there's a chance that they'll make the wrong choice, then we may be able to relax these stiff requirements a bit...
In this backgammon position, white leads 2-1 in a match to 7, and has redoubled. Redoubling was technically an error. The canny opponent would correctly accept the cube, and their equity will be significantly improved. However, if brown erroneously rejects the cube, then they'll have made an even bigger mistake, and we'll have benefited significantly from the whole episode.
This is quantified in a gnubg simulation as a 'bluff potential' of 27%. That means: If we reckon the opponent has a 27% chance of making an incorrect decision, then this 'technical error' would be the correct play 'over the board'.
Publicly, experts would have you believe that playing a phoney is always wrong. They would pretend that the deliberate phoney is so rarely useful that it is hardly worth considering.
Secretly, the experts know that if everyone was well-versed in the nuances of this ploy, it would be even less useful. I reckon that's the real reason it's not covered in detail in The SCRABBLE(tm) Player's Handbook
Of course I'm 99% kidding - and the reality is that a deliberate phoney is only a "technically correct" play when a few unlikely events coincide:
1. PASS looks like it might be better than any other move
2. By passing, you would allow your opponent to make a valuable inference, i.e. - she'd know exactly what you're up to.
3. You can think of a phoney which has good enough score+leave that if left unchallenged, it would be better for you than passing.
4. The information you'd give away by phoneying [and showing those tiles] is no more costly than the information you'd give away by passing.
When you do play a deliberate phoney, you are offering a binary choice to your opponent. They can accept it or reject it. If we assume that they'll always make the right choice, then we must only offer them the choice if we know that either response will still benefit us. However, if there's a chance that they'll make the wrong choice, then we may be able to relax these stiff requirements a bit...
In this backgammon position, white leads 2-1 in a match to 7, and has redoubled. Redoubling was technically an error. The canny opponent would correctly accept the cube, and their equity will be significantly improved. However, if brown erroneously rejects the cube, then they'll have made an even bigger mistake, and we'll have benefited significantly from the whole episode.
This is quantified in a gnubg simulation as a 'bluff potential' of 27%. That means: If we reckon the opponent has a 27% chance of making an incorrect decision, then this 'technical error' would be the correct play 'over the board'.