In return for getting 1000 points from the RIO community I will be doing this PLO trivia thread.

Don't post answers if you haven't figured them out yourself. Correct and incorrect (partial) answers and guesses are allowed though, as long as they're yours. And if nobody will figure one out I will have to post the answers.

1. A classical one: on how many board runout (types) does 3s9s3c3h have the nuts? (Give the board runout (types).)

2. What is the lowest, non-zero, amount of preflop equity that one can have in HU PLO? (Give the exact 4 cards of each player and the equity, and why it is the lowest.)

3. What is the lowest, non-zero, amount of preflop equity that one can have in HU 5-card PLO? (Give the exact 5 cards of each player and the equity, and why it is the lowest.)

4. What is the highest amount of flop equity that one can have in HU PLO, with no outs? (No outs means that the hand currently has a lower hand ranking, and that no turn card can give a higher or equal hand ranking. Give the exact 3 flop cards, 4 cards of each player and the equity, and why it is the highest.)

5. What is the lowest amount of turn equity that one can have in HU PLO with the current best hand? (Give the exact 4 flop and turn cards, 4 cards of each player and the equity, and why it is the lowest.)

6. Is it possible to have a draw on the flop against a made hand, and to have your equity increased on a blank turn that does not give you additional outs? (Give the exact 4 flop and turn cards, 4 cards of each player and the equities.)

7. On how many board runout (types) does KsKcKh9h have the nuts? (Give the board runout (types).)

8. Which PLO hand can make the nuts in the most different ways? (A different way is defined as using two different cards to make a different hand on a different board. For example: 9s8s9h8h can make the nuts on AhKc7d6s5d with 9s8s/9s8h/9h8s/9h8h but they all count as 98, so only once. AcAsTs3s makes the nuts on Ks9s8s3c2h with AsTs/As3s, but they only count once, since they make the ace high flush, and they need the As for that. Making flushes in different suits counts twice. Also KsKcKh9h on  KdTh8d5s2c makes the nuts with KsKc/KsKh/KcKh, but they only count once since our suits don't matter when we have KK. Kickers don't count, KdTh8d5s2c is the same as KdQh8d5s2c, same holds for flushes. And the same holds for KsKcKh9h on 9s9c9d8c8h, it is just one type 999xx. Give the board runout (types).)

9. Which PLO hand can make the nuts in the least different (non-zero) ways?

10. Is there a hand in PLO that has always more than 50% preflop equity in a HU matchup, with the only exception being against itself? (Up to suit symmetry, so Qs9sQhTh and Qc9cQdTd are the same hand: Qx9xQyTy so they only count as one hand. But JsTs9h8h and JcTc9s8s are not the same hand since the first hand has the second dominated in suits.)

11.(i) If the answer to 10. is positive, is the a second best hand that always has morethan 50% preflop equity in a HU matchup, with the only exceptions being against the first best hand or against itself?

11.(ii) If the answer of 11(i) is positive, can this chain be extended to 20 hands? (If we denote hand #1 has more equity than hand #2 by #1 > #2, then a chain is denoted by #1 > #2 > #3 > #4 > ... > #20. Where #1 is the best hand, #2 the second best hand etc. This chain must be transitive, so triangles like #2 > #3, #3 > #4 and #4 > #2 must be ruled out. An example of a triangle in NL is AKo > JTs, JTs > 22, 22 > AKo)

11.(iii) What is the best hand from 'the chain' that can form a triangle? (In the example of #2 > #3, #3 > #4 and #4 > #2 that will be #2, since #2 is part of a triangle with #3 and #4. So that implies that #1 does not form a triangle, and hence #1 > #2, #1 > #4, #1 > #4.)

12. Is it possible to form a 4-cycle with the equity relation from question 11? (This means that #1 > #2, #2 > #3, #3 > #4 and #4 > #1. The relation between #1 and #3 is free, just as the relation between #2 and #4.)

13. is it possible to form a 5-cycle with the equity relation from question 11? (This means that #1 > #2,
#2 > #3, #3 > #4, #4 > #5 and #5 > #1. The relation between #1 and #3/#4 is
free, just as he relation between #2 and #4/#5 etc etc.)

14. On how many board runout (types) does Ts9h8s7h have the nuts? (Give the board runout (types).)