WB 8.16.2 - again
In a recent discussion, one of the points made in favour of a hesitation then a single raise suggest a weak hand was that hands on the borderline of pass / single raise are more common than hands on the single/double raise borderline.
Thus statistically a "borderline indicator" such as a hesitation is more likely to suggest a weak hand than a strong one (for the range shown).
Fair enough.
Similarly, the double raise was thought to be about equal, so no useful inference could be drawn from a hesitation.
So I thought: let's do some stochastic analysis (Monte Carlo) and see what the reality is.
The method I use was simplistic, designed to give an overall feel for the relative probabilities. I looked at 10,000 hands where dealer opens 1H, next player passes, and responder raises in hearts. I assumed a hesitation meant the points were either 5/6, 9/10, 12/13.
For the single raise, a 9/10 point hand is actually twice as likely as a 5/6 point hand (63% v. 37%) - contrary to received wisdom.
For the double raise it's closer, a 9/10 pont hand is 50% more likely than a 12/13 point hand (59% v 41%).. Not as blatant, but still statistically significant.
OK so it's not that simple, but perhaps we should be revisiting those assumed inferences?
It does "feel" like a pause before a single raise shows a weak hand, but that could be just because I've been told that for years and years.
For those who are interested, I had to generate around 2 million hands to generate the 10,000 that met the requirement.
Comments
Hmm. That does make some sense to me, the average is 10HCP and even if you give one hand 13 points for the 1H opener that's only -1 to the rest of the hands. So 8-10 hands should be the most common type.
Admittedly the question is more like "which hand type is most likely to represent a 'problem' hand. But I actually think the 9 HCP hands are the difficult ones, because these are prone to be passed out in a single raise but a stretch for other actions. Whereas with a weak raise it's easy, you just raise.
Ooops - numpty got confused.
The inference of a hesitation then a single raise is indeed as the analysis suggests - something in hand.
The point about the double raise still stands.