to show or not to show (i)

Poker discussion seldom extends to the very last decision of a hand: whether to muck with or without showing. Hardly surprising; after all, it’s tough to analyse, a touch bland and after the fact, somewhat.

‘I’m not giving any more information out than I have to, if they want it they’ll have to pay for it’ is a not unpopular, if rather old school perspective, on the subject. Certainly the assumption of monotonic behaviour discussed previously could explain why, at least in part, this view is held.

The two extreme strategies of full and non-disclosure of hands will inevitably impact on players’ performances in different ways. And, forced to choose between them, the latter option would be preferred over the former by sentient poker players. Therefore one would deduce moving from a covert to an overt strategy to initiate a loss in EV, in value. A graphical representation of this statement would look like this:

What of the points between these two end-states; what would the curve joining them look like? The natural tendency is to approximate to a linear relationship, a straight line, as follows:




Even if the relationship isn’t linear, or strictly monotonically decreasing, it seems likely the next step will be a southerly one. Certainly, with little more to guide you than a couple of stones and a pair of crossed sticks (fig1), it seems a reasonable assumption. Although likely, it isn’t certain; what if it looks something like this?

Everyone’s plot would be different, of course, heavily dependent on which hands were shown, not simply how many. Without evidence, though, it is pure conjecture. Hopefully, in the next article, I will flesh out some fairly obvious reasons to support this view.

Next Article: Part (ii) June 15th

nb: the graphs were edited rather than constructed, so nothing should be read into where the axis intersect - in other words, that showing no hands has zero value and showing all has negative, the absolute values are pretty arbitrary, but not relatively.