expected number of tricks, one need only subtract 2 ZPs and divide by 5. For example, with 52 ZPs, subtracting 2 gives 50, and dividing 50 by 5 gives 10 – the number of tricks expected to be taken. Some players use ZP for suit bidding only. Others use them for bidding no-trump as well. Zar recommends the following scheme. Notice that not having an 8-card fit increases the ZP required for a given level by 5. Grand slam 67+ ZP with fit or 72+ ZP without fit First round control in all suits Small slam 62+ ZP with fit or 67+ ZP without fit First round control of at least three suits Second round control for the suit with no first-round control Notump game All suits stopped 52+ ZP and any 5-3 fit or 4-4 minor fit 57+ ZP without fit Major suit game 52+ ZP and major suit fit Minor suit game 57+ ZP and minor suit fit Does not meet notrump requirements Not more than two quick tricks in any suit Zar Points conversion The simplest way to use Zar Points (in respect of opening hands) is to divide everything by two and open, as Charles Goren taught, with 13 points. Thus we effectively use the same high card point scale devised by the Four Aces in the 1930s with A=3, K=2, Q=1, J=½. We then add the length of the longest suit and finally, we add half the difference in the length of the second and fourth longest suits. The foregoing normalizes Zar Points to numbers more commonly used in Standard American bidding. Alternatively, see the section below: Obtaining the conversion. To get the HCP equivalent discussed above, Zar points need to be scaled. To scale the values of the honors from a 13-point scale to a 10-point scale, the ZP are multiplied by 10/13 and rounded to the nearest half. This results in slightly under valuing aces and jacks but is much more accurate than the traditional count. To scale the shape points to the traditional scale, we can subtract 8 (to set the lowest value at 0) and divide by two (to scale the highest value correctly). Algebraically, if 'a' is the length of the longest suit, 'b' the second longest, and 'd' the shortest: New bidding systems Petkov has proposed a core bidding method, similar to the Precision Club derivatives Symmetric Relay and