Abstract Three experiments tested behavioral properties of risky decision making. In the first, 433 participants received different formats for display of gambles. Within each of three formats, five “new paradoxes” that violate cumulative prospect theory (CPT) were tested. Despite suggestions that theories might be descriptive with these procedures, all five paradoxes persisted in all three formats. A second experiment with 200 participants tested the same properties in gambles on losses. These data also violated CPT but were approximately compatible with the reflection hypothesis. In the third experiment, consequences were framed to produce “mixed” gambles. These data violated CPT, but there were also significant framing effects. Results contradicted four editing principles and implications of original prospect theory. The major findings agree with a transfer of attention exchange model that has also bested CPT in other studies. Combined with other results, there is now a substantial body of evidence with five paradoxes that refute CPT with positive, negative and mixed gambles, involving more than 8000 participants and 14 formats for displaying gambles.