When you are backcounting the total frequency is not 1. You have to count rounds observed but not played as rounds. You may notice Don's charts on page 20 of BJA3 all divide the product of variance times frequency by frequency. Notice the frequency being divided is around 25 to 30 percent. You need the frequency of the counts you just watch and that plus the frequency of the hands you play is 1. The sim data implies you are playing 46% of the total rounds.
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