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Topic: Handicap Order - what beats what? (Read 7145 times) |
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mistre
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Posts: 553
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Re: Handicap Order - what beats what?
« Reply #30 on: Apr 19th, 2008, 3:31pm » |
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on Apr 19th, 2008, 6:50am, woh wrote:Great list, mistre!
I believe those are
MHHC
EHHC
EDDCC
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Great eyes, Woh! I appreciate it! Next time I get a chance, I will add the missing handicaps.
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aaaa
Forum Guru
Arimaa player #958
Posts: 768
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Re: Handicap Order - what beats what?
« Reply #31 on: Apr 19th, 2008, 6:19pm » |
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Unfortunately, using the 3 material evaluators on Janzert's page gives me a considerable amount of ties. Nevertheless, here is the result I get:
001. No handicap
002. R
003. C
004. D
005. RR
006. CR
007. DR
008. RRR
009. H
010. CC
011. CRR
012. DC
013. DRR
014. CCR
""". DD
""". HR
""". RRRR
018. CRRR
019. DCR
020. HC
021. CCRR
""". DCC
""". DDR
""". DRRR
""". HRR
026. HD
027. CRRRR
""". DCRR
""". HCR
""". M
""". RRRRR
032. DDC
033. HCC
""". HDR
""". MR
036. DCCR
""". DDRR
""". HRRR
039. CCRRR
040. DRRRR
041. HCRR
""". HDC
043. DDCR
044. CRRRRR
""". DCRRR
""". HDD
""". HH
""". RRRRRR
049. DCCRR
""". DDRRR
""". HCCR
""". HDRR
""". MC
054. HRRRR
""". MD
""". MRR
057. DDCC
""". HHR
059. CCRRRR
""". MCR
061. DRRRRR
""". HDCR
063. DDCRR
""". HCRRR
065. RRRRRRR
066. HHC
""". MH
068. DCRRRR
""". MCC
""". MDR
071. HDDR
072. HHD
073. HCCRR
074. DCCRRR
""". HDRRR
""". MRRR
077. CRRRRRR
078. DDCCR
""". HDCC
""". HHRR
""". MDC
082. E
083. DDRRRR
""". HRRRRR
085. HDDC
086. MCRR
087. HDCRR
088. DDCRRR
089. DRRRRRR
""". HHCR
091. HCRRRR
092. MDD
093. RRRRRRRR
094. CCRRRRR
""". MHR
096. HCCRRR
097. MCCR
""". MDRR
099. HDDRR
100. DDCCRR
""". HHDR
""". HHRRR
103. HDCCR
""". MRRRR
105. HHCC
106. DCRRRRR
""". HDRRRR
""". MHC
109. CRRRRRRR
""". DCCRRRR
""". MDCR
112. ER
""". HRRRRRR
114. HDCRRR
115. HDDCR
116. HHDC
""". MCRRR
118. HHCRR
119. MDDR
""". MHD
121. DDRRRRR
122. DDCRRRR
123. DRRRRRRR
""". EC
125. MCCRR
""". MDCC
""". MDRRR
128. CRRRRRRRR
""". HHDD
""". MHRR
131. HDDRRR
132. CCRRRRRR
""". HDDCC
134. HDCCRR
135. HCRRRRR
""". HHDRR
137. DDCCRRR
""". HCCRRRR
139. CCRRRRRRR
""". HHCCR
141. MRRRRR
142. HHRRRR
143. ED
144. MHCR
145. MDCRR
""". MDDC
147. DCRRRRRR
148. DRRRRRRRR
149. HDDCRR
""". HDRRRRR
151. HHCRRR
152. DCRRRRRRR
""". HHDCR
""". MCRRRR
""". MHH
156. ERR
""". HDCRRRR
158. DCCRRRRR
""". DCCRRRRRR
""". HRRRRRRR
161. MDDRR
""". MHDR
163. MHCC
164. HHDDR
165. MCCRRR
166. DDRRRRRR
""". HDCCRRR
""". MDCCR
""". MHRRR
170. ECR
171. HDDRRRR
""". HHCCRR
""". MDRRRR
174. HHDRRR
175. HDDCCR
176. HHDCC
177. EH
178. MDDCR
179. DDCRRRRR
""". DDCRRRRRR
""". DDRRRRRRR
""". HCRRRRRR
183. MDCRRR
""". MHCRR
""". MRRRRRR
186. MHDC
187. DDCCRRRRR
""". HHDDC
189. DDCCRRRR
""". HDDCRRR
191. HRRRRRRRR
""". MHHR
193. EDR
194. HHDCRR
195. ECC
""". HHCRRRR
""". HHRRRRR
198. HCCRRRRR
199. HCCRRRRRR
""". HCRRRRRRR
201. MDDRRR
""". MHDD
""". MHDRR
204. MCRRRRR
205. HDRRRRRR
206. CCRRRRRRRR
""". ERRR
""". MDCCRR
""". MDDCC
""". MHCCR
211. EDC
""". HHDDRR
213. MHHC
214. HDCRRRRR
""". HDDCCRR
""". HHDRRRR
""". MCCRRRR
""". MHRRRR
219. HHCCRRR
""". MHHD
221. HDCCRRRR
222. HHDCCR
223. ECRR
224. MDRRRRR
225. MDDCRR
""". MHDCR
227. HDDRRRRR
228. DCRRRRRRRR
""". HDCRRRRRR
230. HDCCRRRRR
""". MHCRRR
232. EDD
""". MDCRRRR
234. HDDRRRRRR
""". HDRRRRRRR
236. HDDCRRRRR
237. EHR
""". HHDDCR
""". MHHRR
240. DCCRRRRRRR
""". HHDCRRR
242. HDDCRRRR
243. MDDRRRR
244. EDRR
245. MHCCRR
""". MRRRRRRR
247. ECCR
""". MDCCRRR
""". MHDDR
""". MHDRRR
251. MDDCCR
252. HHRRRRRR
253. HHCRRRRR
""". HHDDRRR
255. MHDCC
256. EHC
""". HDDCCRRRR
258. HHCCRRRR
""". MHHCR
260. DDRRRRRRRR
261. HHDCCRR
""". MDDCRRR
263. DDCRRRRRRR
""". MCCRRRRR
""". MHRRRRR
266. ERRRR
""". HDDCCRRR
""". MCRRRRRR
""". MHDCRR
270. HHDDCC
271. EDCR
""". HHDRRRRR
273. MHHDR
274. MHCRRRR
275. MHDDC
276. DDCCRRRRRR
277. HCRRRRRRRR
278. HCCRRRRRRR
""". HHDCRRRR
""". HHDDCRR
281. ECRRR
""". MDCRRRRR
""". MDRRRRRR
284. EHD
285. MHHRRR
286. MHCCRRR
""". MHHCC
288. HHCCRRRRR
""". MHDDRR
290. EDDR
291. HHCRRRRRR
""". MDCCRRRR
""". MDDCCRR
""". MHDRRRR
295. HHRRRRRRR
""". MRRRRRRRR
297. MDDRRRRR
""". MHDCCR
299. EHRR
300. EDCC
""". HHDCRRRRR
""". HHDRRRRRR
303. MCCRRRRRR
304. MHHDC
305. EDRRR
306. ECCRR
""". HHDCCRRR
""". HHDDRRRR
""". MCRRRRRRR
310. HDRRRRRRRR
311. HHDDRRRRR
""". MDDCRRRR
""". MHHCRR
314. MHDCRRR
""". MHHDD
316. HDCRRRRRRR
317. HHDCCRRRR
""". MDCCRRRRR
319. HDCCRRRRRR
""". HHDDCCR
""". MHDDCR
322. EHCR
""". HDDRRRRRRR
324. MHCRRRRR
325. EDDC
326. EDCRR
""". HDDCRRRRRR
""". MHHDRR
329. HHDDCRRR
""". MDCRRRRRR
""". MDDCCRRR
""". MHRRRRRR
333. MDRRRRRRR
""". MHCCRRRR
335. ERRRRR
""". MDDCRRRRR
""". MHDDRRR
338. MHHRRRR
339. MHDCCRR
340. EM
341. MDDRRRRRR
342. HHDDCRRRR
343. DCCRRRRRRRR
""". MHDRRRRR
345. MHHCCR
346. ECRRRR
347. EHH
348. EHDR
""". MHDCRRRR
350. HDDCCRRRRR
351. EHCC
""". MHDDCC
353. EDDRR
354. MDDCCRRRR
355. MHHCRRR
356. MHDDCRR
357. EDCCR
""". EHRRR
359. ECCRRR
360. HHDDCCRR
361. EDRRRR
""". MHHDCR
363. MHDCCRRR
364. DDCRRRRRRRR
365. HHDDCCRRR
366. HHRRRRRRRR
367. EDDCR
""". EHDC
""". MHDDRRRR
370. HCCRRRRRRRR
""". HHCRRRRRRR
""". MHCCRRRRR
""". MHHDDR
374. EHCRR
375. MHCRRRRRR
""". MHHDRRR
377. MCCRRRRRRR
378. DDCCRRRRRRR
""". EDCRRR
380. HHCCRRRRRR
""". HHDRRRRRRR
382. MHHCCRR
383. EMR
""". MHRRRRRRR
385. HHDCRRRRRR
""". MCRRRRRRRR
387. MHDRRRRRR
388. ERRRRRR
""". MHDCRRRRR
390. MHHRRRRR
391. MHDDCCR
""". MHHDCC
393. HHDDRRRRRR
""". MHDDCRRR
395. EHDRR
396. EDDRRR
""". EHHR
""". HHDCCRRRRR
""". MHDDRRRRR
400. EHCCR
""". EMC
""". HDCRRRRRRRR
403. ECRRRRR
""". EHDD
405. EDCCRR
""". MDRRRRRRRR
""". MHDCCRRRR
""". MHHCRRRR
409. MDCCRRRRRR
""". MHHDDC
411. HDDRRRRRRRR
""". MDCRRRRRRR
""". MHHDCRR
""". MHHRRRRRR
415. EDDCC
416. EHRRRR
""". MHHCRRRRR
418. HHDDCRRRRR
""". MDDCRRRRRR
420. ECCRRRR
""". MDDRRRRRRR
422. EMD
423. HDCCRRRRRRR
424. MHDDCRRRR
425. MHHDRRRRR
426. EDRRRRR
427. EHDCR
428. HDDCRRRRRRR
429. EDDCRR
""". MHHCCRRR
""". MHHDDRR
432. EHHC
433. MHDDCCRR
""". MHHDRRRR
435. EHCRRR
""". MDDCCRRRRR
""". MHHCCRRRR
438. EMRR
439. EDCRRRR
440. MHHDCRRRR
441. MHHDCCR
442. EDDRRRR
""". EHCCRR
""". EHDDR
""". EHDRRR
""". EHHD
""". HDDCCRRRRRR
448. EHHRR
""". MHCCRRRRRR
""". MHHDDRRRR
451. HHDDCCRRRR
""". MHDDCCRRR
453. EDCCRRR
""". MHCRRRRRRR
455. EMCR
""". ERRRRRRR
457. MHHDCRRR
458. EHDCC
459. EMH
460. EDDCCR
""". HHCRRRRRRRR
462. MHDCRRRRRR
463. HHCCRRRRRRR
464. MHDRRRRRRR
465. EMDR
466. ECRRRRRR
""". EHRRRRR
468. HHDRRRRRRRR
469. MCCRRRRRRRR
""". MHHDCCRRR
""". MHHDDCR
472. MHRRRRRRRR
473. ECCRRRRR
""". MHDDRRRRRR
475. EDDCRRR
""". HHDCRRRRRRR
""". MHDCCRRRRR
478. EHDCRR
479. EHHCR
480. EHCRRRR
""". MHHDDRRR
482. EMCC
483. MHHDDCRRR
484. MHHCRRRRRR
485. DDCCRRRRRRRR
""". EMRRR
""". MHHRRRRRRR
488. EDRRRRRR
""". EHDDC
""". HHDDRRRRRRR
491. MHDDCRRRRR
492. EDCRRRRR
""". HHDCCRRRRRR
""". MHHDCCRR
495. MHHDRRRRRR
496. EHCCRRR
""". MDCCRRRRRRR
498. EMDC
""". MDCRRRRRRRR
500. EHHDR
501. EHDDRR
""". EHDRRRR
503. EHHRRR
504. EDCCRRRR
""". HHDDCRRRRRR
506. MHHCCRRRRR
507. EDDCCRR
""". EHDCCR
""". MDDRRRRRRRR
510. EHHCC
""". MDDCRRRRRRR
""". MHHDDCC
513. EMCRR
514. EDDRRRRR
""". EMHR
516. EMDD
517. MHHDCRRRRR
518. MDDCCRRRRRR
519. MHHDDCRR
520. MHDDCCRRRR
521. EMDRR
522. ECCRRRRRR
523. ECRRRRRRR
524. EHDCRRR
525. MHHDDCCRR
526. EDDCRRRR
527. EHHCRR
""". EHHDC
""". MHHDDRRRRR
530. EHRRRRRR
""". ERRRRRRRR
532. HHDDCCRRRRR
533. EMCCR
534. EHDDCR
535. HDCCRRRRRRRR
536. EHCRRRRR
""". EMHC
538. EMRRRR
539. EDCRRRRRR
540. EDCCRRRRR
""". EHCCRRRR
542. MHHDCCRRRR
543. EHHRRRR
""". HDDCRRRRRRRR
545. EHHDRR
""". EMDCR
""". EMHD
548. EHDDRRR
549. EDDCCRRR
""". EDRRRRRRR
""". EHDCCRR
""". MHCCRRRRRRR
553. EHDRRRRR
""". MHCRRRRRRRR
555. EHHCCR
556. EDDRRRRRR
""". EMHRR
558. EDDCRRRRR
""". EHHDD
560. EMDDR
""". MHHDDCRRRR
562. MHDCCRRRRRR
""". MHDCRRRRRRR
564. EMCRRR
565. HDDCCRRRRRRR
566. EHDCRRRR
567. MHDRRRRRRRR
568. MHHDDCCR
569. EHDDCC
570. EHHCRRR
""". MHDDCRRRRRR
572. EHDDCRR
""". EMHH
574. MHDDRRRRRRR
575. EMDCC
""". EMDRRR
577. EDDCCRRRR
""". EHHDCR
579. MHHCRRRRRRR
580. EMHCR
581. EHDCCRRR
""". EMCCRR
""". MHHRRRRRRRR
584. HHCCRRRRRRRR
585. EHCCRRRRR
586. EMHDR
""". MHHCCRRRRRR
588. EHCRRRRRR
""". EHDDRRRR
""". MHHDRRRRRRR
591. EMDDC
592. EHHDRRR
593. MHDDCCRRRRR
594. EHHRRRRR
""". HHDCRRRRRRRR
596. EHHCCRR
597. EMDCRR
598. EMRRRRR
599. EHRRRRRRR
""". MHHDCRRRRRR
601. EHDCRRRRR
""". EHDRRRRRR
603. ECCRRRRRRR
604. HHDDRRRRRRRR
605. EMCRRRR
606. EMHCC
607. EHDDCCR
""". EMDDRR
609. EHDDCRRR
""". EHHDDR
""". EMHRRR
612. EHHCRRRR
613. EHHDCC
614. MDCCRRRRRRRR
615. ECRRRRRRRR
""". EHDCCRRRR
617. EHDDRRRRR
618. EMHDC
619. EMHHR
620. EDCCRRRRRR
""". EHHDCRR
622. EMDRRRR
""". HHDCCRRRRRRR
624. MHHDDRRRRRR
625. MHHDDCCRRR
626. EDCRRRRRRR
""". MDDCRRRRRRRR
628. EMHDD
629. EMDCCR
630. MHHDCCRRRRR
631. EDDCRRRRRR
""". EHHCCRRR
""". EHHDRRRR
634. EMHCRR
635. HHDDCRRRRRRR
636. EDRRRRRRRR
637. EMCCRRR
638. EHDDCRRRR
639. EHHCRRRRR
640. EDDCCRRRRR
""". EMHDRR
642. EHDDCCRR
643. EMDDCR
""". HHDDCCRRRRRR
645. EHHRRRRRR
646. EDDRRRRRRR
""". MDDCCRRRRRRR
648. EMRRRRRR
649. EHHDDC
""". EMDCRRR
651. EMHHC
652. EMHHD
653. EHHDDRR
""". EMHRRRR
655. EHCCRRRRRR
656. EHHDRRRRR
657. EHHCCRRRR
""". EHHDCCR
""". EMDDRRR
660. MHHDDCRRRRR
661. EHHDCRRR
662. EMCRRRRR
""". EMHCCR
664. EHDDCCRRR
665. EHDCCRRRRR
666. EHCRRRRRRR
667. MHCCRRRRRRRR
668. EHDCRRRRRR
669. EMHHRR
670. EMHDCR
671. EMDRRRRR
672. EMDCCRR
""". MHDCRRRRRRRR
674. EHHDCRRRR
""". EMDDCC
676. EMCCRRRR
""". EMHCRRR
678. EHDRRRRRRR
""". EMHDDR
680. EHRRRRRRRR
681. EHDDRRRRRR
""". EMCRRRRRR
683. EHHDCCRR
684. EMDDCRR
685. EMRRRRRRR
""". MHDCCRRRRRRR
687. ECCRRRRRRRR
""". EMCCRRRRR
""". EMHDRRR
""". MHDDRRRRRRRR
691. EHDDCRRRRR
""". EHHDDCR
""". EMDCRRRR
""". MHDDCCRRRRRR
695. EHHDDRRR
""". EMDCRRRRR
697. EMDRRRRRR
698. MHHCRRRRRRRR
699. EHHDCCRRR
""". EHHDDRRRR
701. EMHHCR
702. HDDCCRRRRRRRR
703. EDCCRRRRRRR
""". MHHDRRRRRRRR
705. EMHHDR
706. EMHDCC
""". MHDDCRRRRRRR
708. EDCRRRRRRRR
709. EMDDRRRR
""". EMDDRRRRR
711. EDDCCRRRRRR
712. EHHCCRRRRR
713. EHDDCCRRRR
714. EHHCRRRRRR
""". EMHRRRRR
716. EMHDDC
717. EMHRRRRRR
718. EMDCCRRRR
719. EDDCRRRRRRR
720. EMDCCRRR
""". EMHCCRR
722. EHHDDCRR
""". MHHCCRRRRRRR
""". MHHDDCCRRRR
725. EHHRRRRRRR
726. EMHCRRRRR
727. EDDRRRRRRRR
""". EMDDCCR
729. EMHHRRR
730. EHHDDCRRR
""". EHHDRRRRRR
732. EMDDCRRRR
733. EHHDCRRRRR
""". EHHDDCC
""". EMHDCRR
""". EMHDRRRRR
737. EHCCRRRRRRR
738. EMDDCRRR
""". MHHDCCRRRRRR
740. EMHCRRRR
""". MHHDCRRRRRRR
742. EHDCCRRRRRR
""". HHDCCRRRRRRRR
744. EMHHCC
745. EHCRRRRRRRR
""". EMHDDRR
747. EMHHDC
748. EMHHDD
749. EHDCRRRRRRR
750. EMHCCRRRR
""". EMHDRRRR
752. EHHDCCRRRR
753. EHDDCRRRRRR
""". EMDDCCRRR
""". MHHDDRRRRRRR
756. EMHHRRRRR
757. EHHDDRRRRR
""". EMHDCRRRR
759. EHDRRRRRRRR
760. MDDCCRRRRRRRR
761. EHDDCCRRRRR
762. EMDDCCRR
""". HHDDCRRRRRRRR
764. EHHDDCCR
765. EMCRRRRRRR
""". EMRRRRRRRR
767. EMCCRRRRRR
""". EMHDDRRRR
769. MHHDDCRRRRRR
770. EHDDRRRRRRR
771. HHDDCCRRRRRRR
772. EHHDDCCRR
""". EMDCRRRRRR
""". EMHHCRR
775. EMHCCRRR
""". EMHDCCR
777. EMDRRRRRRR
778. EMHHDRR
779. EHHCCRRRRRR
780. EDCCRRRRRRRR
781. EMDCCRRRRR
782. EMDDRRRRRR
783. EMHDCCRRR
784. EHHDDCRRRR
785. EHHCRRRRRRR
""". EMHDCRRR
787. EMHHCRRRR
788. EDDCCRRRRRRR
789. EMHDDCR
790. EMHHDRRRR
791. EMHDDCRRR
792. MHDCCRRRRRRRR
793. EDDCRRRRRRRR
""". EHHDCRRRRRR
795. EMDDCRRRRR
""". EMHHRRRR
797. MHHDDCCRRRRR
798. EHHRRRRRRRR
799. EMHCRRRRRR
800. EHHDCCRRRRR
801. EMHDDRRR
802. EHHDRRRRRRR
803. EMHRRRRRRR
804. EHCCRRRRRRRR
""". EMHDRRRRRR
""". MHDDCRRRRRRRR
807. EHDCCRRRRRRR
""". MHDDCCRRRRRRR
809. EMHDCCRR
""". EMHHCCRRR
811. EMDDCCRRRR
812. EMHHDCRRR
813. EMHCCRRRRR
814. EMHHDDRRR
815. EHDCRRRRRRRR
""". EHHDDCCRRR
""". EMHHCCR
818. EHHDDRRRRRR
819. EMHDDCC
820. EMHDDCRR
821. EMCCRRRRRRR
""". EMCRRRRRRRR
""". EMHHDCR
824. EHDDCCRRRRRR
""". EMHDCRRRRR
""". MHHCCRRRRRRRR
827. EHDDCRRRRRRR
""". EHHDDCRRRRR
""". EMHDDCCRR
830. EMHHDDR
831. EMHDDRRRRR
832. EMDCCRRRRRR
""". EMDRRRRRRRR
834. EMHHRRRRRR
""". MHHDCCRRRRRRR
836. EMDCRRRRRRR
""". EMHHCRRR
838. EHDDRRRRRRRR
""". MHHDCRRRRRRRR
840. EHHCCRRRRRRR
841. EMDDCRRRRRR
842. EMDDRRRRRRR
""". EMHDCCRRRR
844. EMHHDRRR
845. EHHCRRRRRRRR
846. EMDDCCRRRRR
847. EHHDDCCRRRR
848. EHHDCCRRRRRR
""". EMHDDCCR
850. EDDCCRRRRRRRR
""". EMHDDCRRRR
852. EMHHDCCRR
""". EMHRRRRRRRR
""". HHDDCCRRRRRRRR
855. EHHDCRRRRRRR
856. EMHHDCC
857. EMHHDDCRR
858. MHHDDCRRRRRRR
859. MHHDDRRRRRRRR
860. EMHHCRRRRR
861. EMHCCRRRRRR
""". EMHHDDC
863. EMHCRRRRRRR
""". EMHHCCRR
865. EHHDRRRRRRRR
""". EMHHDRRRRR
""". MHHDDCCRRRRRR
868. EHHDDCRRRRRR
""". EMHDCRRRRRR
870. EHHDDRRRRRRR
""". EMHDRRRRRRR
872. EMHHDCRR
873. EHDCCRRRRRRRR
874. EMCCRRRRRRRR
""". EMHDCCRRRRR
876. EHHDDCCRRRRR
""". EMHDDRRRRRR
""". EMHHDDRR
879. EMHDDCCRRR
""". EMHHCCRRRR
881. EMDCCRRRRRRR
882. EMDCRRRRRRRR
883. MHDDCCRRRRRRRR
884. EHDDCCRRRRRRR
""". EHDDCRRRRRRRR
""". EMDDCCRRRRRR
887. EMHHDCRRRR
888. EMDDCRRRRRRR
""". EMHDDCRRRRR
890. EMDDRRRRRRRR
""". EMHHRRRRRRR
892. EMHHDDRRRR
893. EHHCCRRRRRRRR
894. EMHHDCCR
895. EMHCRRRRRRRR
896. EHHDCCRRRRRRR
897. EMHHDDCCR
898. MHHDCCRRRRRRRR
899. EMHCCRRRRRRR
""". EMHDRRRRRRRR
""". EMHHDDCR
902. EHHDCRRRRRRRR
903. EMHHCRRRRRR
904. EMHDDCCRRRR
905. EMHHDRRRRRR
906. EMHDCCRRRRRR
907. EMHDCRRRRRRR
""". EMHHDCCRRR
909. EHHDDCRRRRRRR
910. EHHDDRRRRRRRR
911. EHHDDCCRRRRRR
""". EMHHCCRRRRR
913. EMHDDRRRRRRR
""". EMHHRRRRRRRR
""". MHHDDCRRRRRRRR
916. EMDCCRRRRRRRR
917. EMHDDCRRRRRR
""". EMHHDDCRRR
919. MHHDDCCRRRRRRR
920. EMDDCRRRRRRRR
""". EMHHDCRRRRR
922. EHDDCCRRRRRRRR
""". EMDDCCRRRRRRR
924. EMHHDDCC
925. EMHDDCCRRRRR
926. EMHCCRRRRRRRR
""". EMHHCRRRRRRR
928. EMHHDDRRRRR
929. EMHHDRRRRRRR
930. EMHDCRRRRRRRR
931. EHHDCCRRRRRRRR
""". EMHHDDCCRR
933. EMHHDCCRRRR
934. EMHDCCRRRRRRR
""". EMHHCCRRRRRR
936. EMHDDRRRRRRRR
937. EMHHDCRRRRRR
938. EHHDDCRRRRRRRR
939. EMHDDCRRRRRRR
940. EMHHDDCRRRR
941. EMHHCRRRRRRRR
942. EMHDDCCRRRRRR
943. EMDDCCRRRRRRRR
""". EMHHDDRRRRRR
945. EHHDDCCRRRRRRR
946. EMHHDCCRRRRR
947. EMHHDRRRRRRRR
948. EMHHCCRRRRRRR
""". MHHDDCCRRRRRRRR
950. EMHDCCRRRRRRRR
951. EMHHDCRRRRRRR
""". EMHHDDCRRRRR
953. EMHHDDCCRRR
954. EMHDDCRRRRRRRR
955. EMHHDCCRRRRRR
""". EMHHDDRRRRRRR
957. EMHDDCCRRRRRRR
958. EHHDDCCRRRRRRRR
959. EMHHCCRRRRRRRR
960. EMHHDCRRRRRRRR
961. EMHHDDCCRRRR
""". EMHHDDCRRRRRR
963. EMHHDCCRRRRRRR
964. EMHHDDRRRRRRRR
965. EMHDDCCRRRRRRRR
966. EMHHDDCRRRRRRR
967. EMHHDDCCRRRRR
968. EMHHDCCRRRRRRRR
969. EMHHDDCCRRRRRR
970. EMHHDDCRRRRRRRR
971. EMHHDDCCRRRRRRR
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Arimabuff
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Arimaa player #2764
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Re: Handicap Order - what beats what?
« Reply #32 on: Apr 19th, 2008, 7:19pm » |
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on Apr 19th, 2008, 6:19pm, aaaa wrote:Unfortunately, using the 3 material evaluators on Janzert's page gives me a considerable amount of ties. Nevertheless, here is the result I get:
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With all due respect, that list doesn't make any sense in the extreme part of the handicaps as is often the case with formulas applied too systematically. It says that ONE CAT is weaker than TWO rabbits yet ONE CAT plus ONE RABBIT is STRONGER THAN Three rabbits. How can anybody rely on such absurd results? Either the difference between two rabbits or a cat is so insignificant that it would explain the bizarre switch or we are in the domain of the formula where the uncertainty outweighs the significant part of the number. Something like .5 give or take 1 for a number for instance. That happens all the time in mathematics, the data is so lacking in precision that you start getting results that don't make any sense.
Besides another thing that makes me think that the formula is based on a systematic application that is detached from reality is that you need at least one rabbit in your pieces or you have lost the game BEFORE you even started so when you stop to think about it how can the program even judge that a lone cat is stronger than a lone rabbit when the lone cat means that you have exactly ZERO chance of winning the game? That doesn’t make any sense. I say that formula is unreliable when it comes to BIG handicaps and shouldn’t be used to settle a dispute. In fact, there is also one detail that isn’t taken into account in your formula and that is that I WAS THE FIRST to come up with my result, that should count for something. Had 99 won the three rabbit first we wouldn’t even be having this discussion. I found a solution to a problem that 99 was UNABLE to resolve with less than FOUR rabbits plus a CAT, a solution that put it down to ONE rabbit and one CAT. And I’d have known how to solve the three rabbit problem if I had been informed that it was a possibility. You keep forgetting that the only reason 99 got the three rabbit and not I, is because that I didn’t know that I needed to resolve it. This is a case that we have NEVER encountered in handicap situations.
Someone not getting a record not because of lack of skill or unwillingness but because of not being made aware that he was to get it. In my game all the problems are resolved I would have found the solution even faster than 99 because I had already studied the case. I am the true holder of the record be it CR or RRR they both belong to me because I have being deceived into believing that I had won. Nobody neither 99 nor anyone else said anything about the record being beatable. In American law, you have something that can nullify a trial that is called “unfair surprise”, well that’s exactly what happened to me I have been robbed of the result because of unfair surprise and not beaten on skills but on that stupid unfair surprise and nothing else. 99 merits are exactly ZERO in that affair. If you take a look at his solution you can see that a child could have deduce is from mine. Before my attempt 99 didn’t even DARE to try with less than cat plus FOUR rabbits and all of a sudden THANKS TO ME he tries three rabbits!!! What made him make that leap of faith between FOUR rabbits plus cat to THREE rabbits without CAT. I have been dispossessed of my victory by something that disgusts me just to think about it. Ever see Amadeus? I am Mozart been stolen his final requiem by a poisonous Salieri, that’s what I am. Whatever way you look at it, the hall of fame belongs to me on that one. Salieri didn’t even know that he could do it with less than FOUR rabbits and a CAT before I came along and now since as Mozart was himself I am hated by some here, I will be deprived of my due victory because of that travesty of a contest.
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| « Last Edit: Apr 19th, 2008, 7:20pm by Arimabuff » |
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Arimabuff
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Re: Handicap Order - what beats what?
« Reply #33 on: Apr 19th, 2008, 8:31pm » |
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To sum up what I said in a few words. This case is pretty simple. I did come up with the solution to CR and that solution slightly adapted also works for RRR. I didn't play the latter NOT because I couldn't or was unwilling to but because I DIDN'T KNOW that I HAD TO. That’s the only reason. There is no way in hell that 99 could have had this RRR game if not for me being kept in the dark, be it accidentally or on purpose is not really the point. The point is that the reason why 99 played this game and NOT ME has nothing to do whatsoever with merits and everything to do with someone being deprived of his due victory. The CR belongs to me as well as the RRR which is only a variation of it. Thanks to me 99 knew how the rabbits of Gnobot would react because they reacted in both cases mine and his in a similar fashion. I am sick of having to explain again and again something that is so obvious. It doesn't matter actually if 99 did what he did on purpose or because he is just lacking of a conscience that tells him that some things cross a line. The result is that I have been deprived of my due victory in both cases. Because I didn't have the information that it was even useful for me to play this game.
NOBODY here has ever been subjected to an injustice like that. Have a shred of honesty and ADMIT IT!!! The fact that you don't like me shouldn't be factored in unless you consider that Arimaa is a popularity contest where merits take a back seat. However, if you do then you are a far worse people than I'll ever be!!!!
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| « Last Edit: Apr 19th, 2008, 9:01pm by Arimabuff » |
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IdahoEv
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Re: Handicap Order - what beats what?
« Reply #34 on: Apr 20th, 2008, 1:04pm » |
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on Apr 18th, 2008, 5:11pm, aaaa wrote:| I'm planning to come up with my own material evaluator in the form of a multilayer perceptron based on game statistics. Here's hoping it will have better output than garbage. |
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You'll need to keep the number of nodes in that network very low, otherwise you'll overtrain badly. There just isn't enough data.
The number of possible material state combinations is extremely high, and the majority of them have never occurred in any game. I discovered this when I did research in 2006 into optimizing the coefficients of material evaluators based on the game statistics. Even when there were only a few coefficients, like DAPE which has 7 coefficients, we saw some bad overtraining and/or sensitivity to data selection, and had to start implementing interesting constraints on the selection of games we used in order to get results that made any sense.
At some point soon, I hope to re-run those numbers, by the way. There have been two more years of games now, it would be nice to see if the results have changed significantly.
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| « Last Edit: Apr 20th, 2008, 1:08pm by IdahoEv » |
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IdahoEv
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Re: Handicap Order - what beats what?
« Reply #35 on: Apr 20th, 2008, 1:17pm » |
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Just a quick mention that I would personally much disregard all the results in this thread that used results from the original formulations of DAPE and FAME. When I dug into this in 2006 I found that those algorithms misrepresented the results from real games relative to algorithms with correctly tuned coefficients.
Using the ones on Janzert's calendar, the improvement (in terms of correctly predicting the outcome of games in the database) of optimized DAPE, or LinearAB (my function) over DAPE or FAME was significantly greater than the improvement DAPE or FAME gives over simply counting all the pieces (i.e. considering all pieces worth 1.0 point regardless of size).
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mistre
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Re: Handicap Order - what beats what?
« Reply #36 on: Apr 20th, 2008, 4:26pm » |
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If you rank the 114 major handicaps for the LinearAB function, I can redo the analysis using only LinearAB and DAPE (optimized).
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Janzert
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Re: Handicap Order - what beats what?
« Reply #37 on: Apr 20th, 2008, 4:42pm » |
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on Apr 20th, 2008, 1:17pm, IdahoEv wrote:| Using the ones on Janzert's calendar, the improvement (in terms of correctly predicting the outcome of games in the database) of optimized DAPE, or LinearAB (my function) over DAPE or FAME was significantly greater than the improvement DAPE or FAME gives over simply counting all the pieces (i.e. considering all pieces worth 1.0 point regardless of size) |
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I've never been convinced that this wasn't simply because of overfitting. I think the number of games and range of games we have available is still just too small to try and train a general method from.
Janzert
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IdahoEv
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Re: Handicap Order - what beats what?
« Reply #38 on: Apr 20th, 2008, 7:07pm » |
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on Apr 20th, 2008, 4:42pm, Janzert wrote:
I've never been convinced that this wasn't simply because of overfitting. I think the number of games and range of games we have available is still just too small to try and train a general method from.
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Anything's possible. But LinearAB only has two parameters, A (the cat-to-rabbit ratio) and B (the ratio used for all subsequent levels; i.e. D/C, H/D, M/H and E/M). And it's pretty hard to overfit data with only two coefficients.
Maybe when I get around to rerunning this I can use some part of the data for overfit testing during the optimization. I doubt we'll see much difference. When we looked at the particular cases that the optimized functions preferred over the guessed-at ones, they seemed pretty reasonable to me.
Rather than overfitting, I think you could make a better case that the games themselves don't actually represent the true value of the pieces very well; Karl made a good argument from causality in this vein. (i.e. if getting ahead and being likely to win, or simply being a stronger player, makes certain captures more likely irrespective of winning, it would make those captures appear arbitrarily valuable in the analysis.)
But that's a fundamental limitation of using statistics from the games to answer questions like these. There isn't really anything you can do about it.
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IdahoEv
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Re: Handicap Order - what beats what?
« Reply #39 on: Apr 20th, 2008, 7:21pm » |
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on Apr 20th, 2008, 4:26pm, mistre wrote:If you rank the 114 major handicaps for the LinearAB function, I can redo the analysis using only LinearAB and DAPE (optimized).
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If you want to do it, here's how LinearAB will rank the pieces. For the case of beginning-game sacrifice, you can simply add the following values of the pieces to achieve the LinearAB score. (A=1.241, B=1.316).
rabbit 1.000
cat 1.241
dog 1.633
horse 2.149
camel 2.828
elephant 3.722
(Note that this won't give you the correct LinearAB score once the opponent starts losing pieces because it will ignore 'level collapse', i.e. the fact that EHHRerrr is functionally identical to ECCRerrr. But for game-start sacrifice, there is no level collapse because the opposing team is full.)
I'm sure this system misvalues elephants because the E/M ratio is fixed to B. When I made an alternate optimization that allowed E to vary independently it settled on E~7.5. I doubt that's anything like accurate, though, because there are so few actual examples of E sacrifice to compare against.
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99of9
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Re: Handicap Order - what beats what?
« Reply #40 on: Apr 20th, 2008, 8:10pm » |
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on Apr 20th, 2008, 7:07pm, IdahoEv wrote:| But that's a fundamental limitation of using statistics from the games to answer questions like these. There isn't really anything you can do about it. |
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I agree, and because of this limitation, I think you should be slower to "disregard" the evals which were hand optimized by experts! I'm looking forward to getting back to this conversation when you've run with more data.
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mistre
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Re: Handicap Order - what beats what?
« Reply #41 on: Apr 20th, 2008, 8:59pm » |
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Since there is disagreement on this one, I will take a back seat for now and let you guys sort out which evals are more reliable than others. Is there any way to compare their predictions with real games and see which one was better?
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IdahoEv
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Re: Handicap Order - what beats what?
« Reply #42 on: Apr 20th, 2008, 9:08pm » |
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on Apr 20th, 2008, 8:10pm, 99of9 wrote:
I agree, and because of this limitation, I think you should be slower to "disregard" the evals which were hand optimized by experts! |
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Fair enough, that.
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IdahoEv
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Re: Handicap Order - what beats what?
« Reply #43 on: Apr 20th, 2008, 9:17pm » |
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on Apr 20th, 2008, 8:59pm, mistre wrote: Is there any way to compare their predictions with real games and see which one was better?
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Yes, it's possible, and that is in fact how the coefficients for LinearAB and Optimized DAPE were developed. Existing evals were repeatedly modified (by tweaking the numbers) and measured as to how well they predicted the eventual winner in real games from the database. That cycle was repeated until the eval functions stopped getting "better".
At the end of that process on several eval functions, Optimized DAPE (as implemented on Janzert's page) was the best overall at guessing the winner among games in the history database. LinearAB was a bit behind that in 2nd place. Both did much better than the hand-coded versions.
The debate is whether or not that process is valid in order to determine a material eval function. Karl and Toby are less sure about that than I am. I recognize their concerns that might make the process invalid, but I suspect it still is. There's no way to prove it one way or the other. 
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| « Last Edit: Apr 20th, 2008, 9:18pm by IdahoEv » |
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mistre
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Re: Handicap Order - what beats what?
« Reply #44 on: Apr 20th, 2008, 9:36pm » |
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Were the game that were looked at human vs human games? bot vs bot games? human vs bot games? or all 3?
I can't wait to see what your results will bring when you re-run the analysis. There are quite a few more E handicap games in the database, thanks to me. 
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