Add ponder support

[eduherminio]

Ponder enabled vs no pondering 👎🏽👎🏽

Finished game 163 (Lynx-add-ponder-support-1877-win-x64 vs Lynx 1875 - main): * {No result}
Score of Lynx-add-ponder-support-1877-win-x64 vs Lynx 1875 - main: 13 - 120 - 26  [0.164] 159
...      Lynx-add-ponder-support-1877-win-x64 playing White: 10 - 55 - 15  [0.219] 80
...      Lynx-add-ponder-support-1877-win-x64 playing Black: 3 - 65 - 11  [0.108] 79
...      White vs Black: 75 - 58 - 26  [0.553] 159
Elo difference: -283.6 +/- 62.6, LOS: 0.0 %, DrawRatio: 16.4 %
SPRT: llr -2.26 (-78.0%), lbound -2.25, ubound 2.89 - H0 was accepted

Regression: disabled vs no pondering

Score of Lynx-add-ponder-support-1877-win-x64 vs Lynx 1875 - main: 5153 - 5157 - 6970  [0.500] 17280
...      Lynx-add-ponder-support-1877-win-x64 playing White: 3512 - 1673 - 3455  [0.606] 8640
...      Lynx-add-ponder-support-1877-win-x64 playing Black: 1641 - 3484 - 3515  [0.393] 8640
...      White vs Black: 6996 - 3314 - 6970  [0.607] 17280
Elo difference: -0.1 +/- 4.0, LOS: 48.4 %, DrawRatio: 40.3 %
SPRT: llr 2.9 (100.4%), lbound -2.25, ubound 2.89 - H1 was accepted

So at least just need to fix the pondering behavior, but when it's off the perf isn't affected

Fix pondering: save previous position command and use it to restore Game instance before search after ponder hit
0f440ca

Score of Lynx-add-ponder-support-1948-win-x64 vs Lynx 1941 - main: 232 - 99 - 163  [0.635] 494
...      Lynx-add-ponder-support-1948-win-x64 playing White: 140 - 30 - 77  [0.723] 247
...      Lynx-add-ponder-support-1948-win-x64 playing Black: 92 - 69 - 86  [0.547] 247
...      White vs Black: 209 - 122 - 163  [0.588] 494
Elo difference: 95.9 +/- 25.6, LOS: 100.0 %, DrawRatio: 33.0 %
SPRT: llr 2.91 (100.7%), lbound -2.25, ubound 2.89 - H1 was accepted

Player: Lynx-add-ponder-support-1948-win-x64
   "Draw by 3-fold repetition": 97
   "Draw by fifty moves rule": 13
   "Draw by insufficient mating material": 46
   "Draw by stalemate": 3
   "Draw by stalled connection": 2
   "Draw by timeout": 2
   "Loss: Black loses on time": 4
   "Loss: Black makes an illegal move: d4d3": 1
   "Loss: Black mates": 24
   "Loss: Black's connection stalls": 3
   "Loss: White loses on time": 2
   "Loss: White makes an illegal move: d3e4": 1
   "Loss: White mates": 61
   "Loss: White's connection stalls": 3
   "No result": 7
   "Win: Black loses on time": 3
   "Win: Black mates": 90
   "Win: White loses on time": 2
   "Win: White mates": 137
Player: Lynx 1941 - main
   "Draw by 3-fold repetition": 97
   "Draw by fifty moves rule": 13
   "Draw by insufficient mating material": 46
   "Draw by stalemate": 3
   "Draw by stalled connection": 2
   "Draw by timeout": 2
   "Loss: Black loses on time": 3
   "Loss: Black mates": 90
   "Loss: White loses on time": 2
   "Loss: White mates": 137
   "No result": 7
   "Win: Black loses on time": 4
   "Win: Black makes an illegal move: d4d3": 1
   "Win: Black mates": 24
   "Win: Black's connection stalls": 3
   "Win: White loses on time": 2
   "Win: White makes an illegal move: d3e4": 1
   "Win: White mates": 61
   "Win: White's connection stalls": 3
Finished match

Remove special ponder hit treatment
and

Make sure to cancel ponder search on new game and avoid fake ponder h…Finished game 235 (Lynx-add-ponder-support-1950-win-x64 vs Lynx-add-ponder-support-1948-win-x64): 1-0 {White mates}

cutechess crashes

Try again ponder hit logic of reusing killers and not deleting history

Score of Lynx-add-ponder-support-2025-win-x64 vs Lynx 2024 - main: 210 - 77 - 131  [0.659] 418
...      Lynx-add-ponder-support-2025-win-x64 playing White: 123 - 27 - 59  [0.730] 209
...      Lynx-add-ponder-support-2025-win-x64 playing Black: 87 - 50 - 72  [0.589] 209
...      White vs Black: 173 - 114 - 131  [0.571] 418
Elo difference: 114.5 +/- 28.4, LOS: 100.0 %, DrawRatio: 31.3 %
SPRT: llr 2.9 (100.2%), lbound -2.25, ubound 2.89 - H1 was accepted

Player: Lynx-add-ponder-support-2025-win-x64
   "Draw by 3-fold repetition": 81
   "Draw by fifty moves rule": 15
   "Draw by insufficient mating material": 30
   "Draw by stalled connection": 3
   "Draw by timeout": 2
   "Loss: Black loses on time": 1
   "Loss: Black mates": 25
   "Loss: Black's connection stalls": 1
   "Loss: White loses on time": 1
   "Loss: White mates": 48
   "Loss: White's connection stalls": 1
   "No result": 3
   "Win: Black loses on time": 3
   "Win: Black mates": 84
   "Win: White loses on time": 3
   "Win: White mates": 120
Player: Lynx 2024 - main
   "Draw by 3-fold repetition": 81
   "Draw by fifty moves rule": 15
   "Draw by insufficient mating material": 30
   "Draw by stalled connection": 3
   "Draw by timeout": 2
   "Loss: Black loses on time": 3
   "Loss: Black mates": 84
   "Loss: White loses on time": 3
   "Loss: White mates": 120
   "No result": 3
   "Win: Black loses on time": 1
   "Win: Black mates": 25
   "Win: Black's connection stalls": 1
   "Win: White loses on time": 1
   "Win: White mates": 48
   "Win: White's connection stalls": 1

[eduherminio]

Issue with original impl detecting score 0
logs-draw-detection.txt

[eduherminio]

Issue with 0f440ca:

• logs-illegal-pv.txt
• potential_illegal_move.txt

[eduherminio]

Closing in favor of #772