I think the only way it’s a non-zero chance of taking first is if it was the incomplete person who finished, they were ahead of you, but are now behind you. If the incomplete person still hasn’t finished (but someone else did), I think your chances of taking first are still zero.
If I understand the scenario correctly, I think it is possible. In fact, I believe you can finish under 50%, have no partial finishes and still win.
Suppose player X plays, then AA, then player Y.
After X and AA play, there are 11 pushes, X scored better on three boards, and AA scored better on two boards.
AA is now at (11x50% + 3x0% + 2x100%)/16 =~ 46.9%, with X at 53.1%.
Then player Y plays, pushing the same 11 boards, scoring below both players on the three boards X outscored AA, and scoring between the two when AA outscored player X.
AA =(11x50% + 3x50% + 2x100%)/16 = 56.25%
X = (11x50% + 3x100%+2x0%)/16 = 53.125%
Y = (11x50% + 3x0% + 2x50%)/16 =40.625%
So, AA wins.
As unlikely as it would be, I thought it possible that
- I could score 50.57%
- Someone else could score 49.43%
- Anyone else could score 50.00%
I think the lowest section top I’ve ever seen is 52-something so I think the above scenario is quite low even with 5 players.
I beat procrastinator by 26, NN by 5. Both, and the regular challenge, reissued.
WTF? I know I reissued the declare-only challenge last night, but it’s disappeared, so I just reissued it. JEB_SW and oirg are out. Oops. While I feel sure I correctly did matchpoints yesterday, the one I issued tonite is imps.
Interesting. The math makes sense. My simple minded assumption was that if you finish at <50%, then at least one person is ahead of you that has also finished. And no matter what the next person does, you can’t ever pass that person that is ahead of you. But what you’re saying makes sense in terms of relative positioning of the final player.
The only thing in your scenario that doesn’t make sense is that the end result is AA winning. I almost never do well in the declare-only MP group challenge.
win by 42 vs AA. Reissued
Ouch.
The most recent IMP challenge was dullsville.
Talk about low scoring. I win the regular challenge with just +4.25, by 1.25. Tied 15-15 with procrastinator. Both reissued
AA wins the declare-only (IMPs) with +2.25, the only positive score. Reissued, matchpoints, Klaymen and procrastinator out. I lose by 18 to NN. Reissued
I win the regular challenge with +12.32, by 9.99. I lose to procrastinator by 4. Both reissued
Ironic that I win the Declare-only when it is accidentally IMPs. And I have been the one to advocate for doing MPs for Declare-only, and usually get smoked in MP, D-o.
I with the declare-only with 52.08%, by 1.04%. I lose to NN by 3. Both reissued, with oirg and AA out in the group challenge (imps).
AA wins the regular challenge with +15.50, by 11.75. I beat AA by 8 and lose to procrastinator by 2. :swear: Not the only swing, but the biggest, 13 imps. At my table, E played 4S, making 5, vul. At procrastinator’s W played 3S, down 1. Bidding was different, but IMO the bidding at my table should have made it harder for declarer to guess correctly (between a simple finesse or a ruffing finesse). But against me, declarer took the simple finesse. Against procrastinator, he took the ruffing finest.
All reissued.
Klaymen wins the declare-only with 12,33, by 9.66. I beat NN by 19. Both reissued, NN and JEB_SW out in the declare-only.
I win the regular challenge with +14.75, by 7.00. Reissued
I beat NN by 5, despite letting 3NT make against me when he set 1NT (played from the other side) 1 trick.
Thoughtful defense by me.
spoilertext
(Based on a very old Bridge World article RATS by Betty Kaplan, which described code words Edgar used with her to avoid obvious displeasure. I can’t remember what R was, “Reasonable” probably. A was “Attractive”, T was Thoughtful, S was “Scintillating”. Those were in increasing order of badness. She described a serious of hands where her plays were increasingly bad, culminating in one where during the hand on defense she led the club 9 through declarer, from J9x, which Edgar won but couldn’t read. Edgar’s comment was along the lines of “The club 9!! You had to lead the club 9!!! That play was absolutely…” when he realized that (at least double dummy), the club 9 would beat the contract and was the only card that would beat it. So Betty finished “… Scintillating”.
Maybe not true, but a good story.
In the BBO match, I unblocked an honor when clearly declarer would have played differently if the unblock were necessary, and as it was the unblock was declarer’s only source of 9th trick. Fortunately not vulnerable.
I win the declare-only, which unintentionally was IMPs, with +7.67, by 2.67. Reissued, this time intentionally IMPs, with Klaymen and AA out.
I win the regular challenge with +15.25, by 14.50. I beat AA by 30. Both reissued