{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TZYCSFBNLN3WAZPRCY5NICE4P3","short_pith_number":"pith:TZYCSFBN","canonical_record":{"source":{"id":"1612.07547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-12-22T11:24:09Z","cross_cats_sorted":[],"title_canon_sha256":"07ace2017608a4bbbe1637971990402f4627f4c2d84aad51487b3e3ced57150f","abstract_canon_sha256":"da52becc8401c63e359db554263cf6d8f18ddd0c12b0175e522c4df585cb1ffb"},"schema_version":"1.0"},"canonical_sha256":"9e7029142d5b776065f1163ad4089c7ec4b3a0452896e07ea29ef289dcd21b15","source":{"kind":"arxiv","id":"1612.07547","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07547","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07547v2","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07547","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"TZYCSFBNLN3W","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TZYCSFBNLN3WAZPR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TZYCSFBN","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TZYCSFBNLN3WAZPRCY5NICE4P3","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-12-22T11:24:09Z","cross_cats_sorted":[],"title_canon_sha256":"07ace2017608a4bbbe1637971990402f4627f4c2d84aad51487b3e3ced57150f","abstract_canon_sha256":"da52becc8401c63e359db554263cf6d8f18ddd0c12b0175e522c4df585cb1ffb"},"schema_version":"1.0"},"canonical_sha256":"9e7029142d5b776065f1163ad4089c7ec4b3a0452896e07ea29ef289dcd21b15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:15.271184Z","signature_b64":"A0lyQuRYJihuYq/oYFeNV/JtcmpHjtJMJ1XE4goQifm7lcaMFhTCJyDEpyOuCN5XPG0R3hmhfKY0IhTVrpFPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e7029142d5b776065f1163ad4089c7ec4b3a0452896e07ea29ef289dcd21b15","last_reissued_at":"2026-05-18T00:53:15.270783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:15.270783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07547","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZwCfjl+vEUl67UEh6OSzkKHeOSTDc7gptcSb2Y+CgtRl35RfCsDg3buVkJnN/UB0QHa/g9VX8UENKdszalWdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:41:58.247691Z"},"content_sha256":"f397b56bef59cd584a7cb76f4643cec64be8e8729c1bcb79157c7f35a710d16f","schema_version":"1.0","event_id":"sha256:f397b56bef59cd584a7cb76f4643cec64be8e8729c1bcb79157c7f35a710d16f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TZYCSFBNLN3WAZPRCY5NICE4P3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium Approximation Quality of Current No-Limit Poker Bots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Michael Bowling, Viliam Lisy","submitted_at":"2016-12-22T11:24:09Z","abstract_excerpt":"Approximating a Nash equilibrium is currently the best performing approach for creating poker-playing programs. While for the simplest variants of the game, it is possible to evaluate the quality of the approximation by computing the value of the best response strategy, this is currently not computationally feasible for larger variants of the game, such as heads-up no-limit Texas hold'em. In this paper, we present a simple and computationally inexpensive Local Best Response method for computing an approximate lower bound on the value of the best response strategy. Using this method, we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07547","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bgZHG46YCu0uMmQHprKndyZ30WNRVodNSQppJUuydR6J9i+QV3mb5eekRWMIXF9VNOD4E5P/Xr+RuYltw27xAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:41:58.248044Z"},"content_sha256":"1d0f95d2ad05fed9df77b38e7beaa89fde3501a3721f1440ea96b7624d7da70d","schema_version":"1.0","event_id":"sha256:1d0f95d2ad05fed9df77b38e7beaa89fde3501a3721f1440ea96b7624d7da70d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZYCSFBNLN3WAZPRCY5NICE4P3/bundle.json","state_url":"https://pith.science/pith/TZYCSFBNLN3WAZPRCY5NICE4P3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZYCSFBNLN3WAZPRCY5NICE4P3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T09:41:58Z","links":{"resolver":"https://pith.science/pith/TZYCSFBNLN3WAZPRCY5NICE4P3","bundle":"https://pith.science/pith/TZYCSFBNLN3WAZPRCY5NICE4P3/bundle.json","state":"https://pith.science/pith/TZYCSFBNLN3WAZPRCY5NICE4P3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZYCSFBNLN3WAZPRCY5NICE4P3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TZYCSFBNLN3WAZPRCY5NICE4P3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"da52becc8401c63e359db554263cf6d8f18ddd0c12b0175e522c4df585cb1ffb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-12-22T11:24:09Z","title_canon_sha256":"07ace2017608a4bbbe1637971990402f4627f4c2d84aad51487b3e3ced57150f"},"schema_version":"1.0","source":{"id":"1612.07547","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07547","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07547v2","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07547","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"TZYCSFBNLN3W","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TZYCSFBNLN3WAZPR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TZYCSFBN","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:1d0f95d2ad05fed9df77b38e7beaa89fde3501a3721f1440ea96b7624d7da70d","target":"graph","created_at":"2026-05-18T00:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Approximating a Nash equilibrium is currently the best performing approach for creating poker-playing programs. While for the simplest variants of the game, it is possible to evaluate the quality of the approximation by computing the value of the best response strategy, this is currently not computationally feasible for larger variants of the game, such as heads-up no-limit Texas hold'em. In this paper, we present a simple and computationally inexpensive Local Best Response method for computing an approximate lower bound on the value of the best response strategy. Using this method, we show th","authors_text":"Michael Bowling, Viliam Lisy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-12-22T11:24:09Z","title":"Equilibrium Approximation Quality of Current No-Limit Poker Bots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07547","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f397b56bef59cd584a7cb76f4643cec64be8e8729c1bcb79157c7f35a710d16f","target":"record","created_at":"2026-05-18T00:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"da52becc8401c63e359db554263cf6d8f18ddd0c12b0175e522c4df585cb1ffb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-12-22T11:24:09Z","title_canon_sha256":"07ace2017608a4bbbe1637971990402f4627f4c2d84aad51487b3e3ced57150f"},"schema_version":"1.0","source":{"id":"1612.07547","kind":"arxiv","version":2}},"canonical_sha256":"9e7029142d5b776065f1163ad4089c7ec4b3a0452896e07ea29ef289dcd21b15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e7029142d5b776065f1163ad4089c7ec4b3a0452896e07ea29ef289dcd21b15","first_computed_at":"2026-05-18T00:53:15.270783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:15.270783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A0lyQuRYJihuYq/oYFeNV/JtcmpHjtJMJ1XE4goQifm7lcaMFhTCJyDEpyOuCN5XPG0R3hmhfKY0IhTVrpFPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:15.271184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07547","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f397b56bef59cd584a7cb76f4643cec64be8e8729c1bcb79157c7f35a710d16f","sha256:1d0f95d2ad05fed9df77b38e7beaa89fde3501a3721f1440ea96b7624d7da70d"],"state_sha256":"8b6fc7effb6d277581975afb61bcc5c2b4726a1e08d9b2544b80c5787608e490"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/70jkFD9yc9hiRm6h7gWuTEUT0NCCm9SJl2Ump5bvZygeQyVFatpY58YULSS8hNb82HXk6ZSN/XOTcSFqM08Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:41:58.249996Z","bundle_sha256":"f5ef4d92cb4f9848da582f802bbdd5b25fa895345bef299bc84bb1fa165853b6"}}