Is this AI analysis of a 5 game losing streak correct?

So if the AI cannot understand your concept of accuracy and bow it relates to winning probabilities, maybe you can explain it to us?

This thread has some vlad vibes for sure!

chess is not about probability bro,probability is mathematics and mathematics is not fully chess

@Clownboots said in #1:

Game 1: Opponent Elo = 2259
EA=11+10(2259−2296)/400=11+10−37/400=11+10−0.0925≈11+0.807≈0.553E_A = \frac{1}{1 + 10^{(2259 - 2296)/400}} = \frac{1}{1 + 10^{-37/400}} = \frac{1}{1 + 10^{-0.0925}} \approx \frac{1}{1 + 0.807} \approx 0.553E_A = \frac{1}{1 + 10^{(2259 - 2296)/400}} = \frac{1}{1 + 10^{-37/400}} = \frac{1}{1 + 10^{-0.0925}} \approx \frac{1}{1 + 0.807} \approx 0.553
Probability of losing: 1−0.553=0.4471 - 0.553 = 0.4471 - 0.553 = 0.447
.

Game 2: Opponent Elo = 2220
EA=11+10(2220−2296)/400=11+10−76/400≈11+0.676≈0.597E_A = \frac{1}{1 + 10^{(2220 - 2296)/400}} = \frac{1}{1 + 10^{-76/400}} \approx \frac{1}{1 + 0.676} \approx 0.597E_A = \frac{1}{1 + 10^{(2220 - 2296)/400}} = \frac{1}{1 + 10^{-76/400}} \approx \frac{1}{1 + 0.676} \approx 0.597
Probability of losing: 1−0.597=0.4031 - 0.597 = 0.4031 - 0.597 = 0.403
.

Game 3: Opponent Elo = 2104
EA=11+10(2104−2296)/400=11+10−192/400≈11+0.331≈0.751E_A = \frac{1}{1 + 10^{(2104 - 2296)/400}} = \frac{1}{1 + 10^{-192/400}} \approx \frac{1}{1 + 0.331} \approx 0.751E_A = \frac{1}{1 + 10^{(2104 - 2296)/400}} = \frac{1}{1 + 10^{-192/400}} \approx \frac{1}{1 + 0.331} \approx 0.751
Probability of losing: 1−0.751=0.2491 - 0.751 = 0.2491 - 0.751 = 0.249
.

Game 4: Opponent Elo = 2260
EA=11+10(2260−2296)/400=11+10−36/400≈11+0.813≈0.552E_A = \frac{1}{1 + 10^{(2260 - 2296)/400}} = \frac{1}{1 + 10^{-36/400}} \approx \frac{1}{1 + 0.813} \approx 0.552E_A = \frac{1}{1 + 10^{(2260 - 2296)/400}} = \frac{1}{1 + 10^{-36/400}} \approx \frac{1}{1 + 0.813} \approx 0.552
Probability of losing: 1−0.552=0.4481 - 0.552 = 0.4481 - 0.552 = 0.448
.

Game 5: Opponent Elo = 2161
EA=11+10(2161−2296)/400=11+10−135/400≈11+0.464≈0.683E_A = \frac{1}{1 + 10^{(2161 - 2296)/400}} = \frac{1}{1 + 10^{-135/400}} \approx \frac{1}{1 + 0.464} \approx 0.683E_A = \frac{1}{1 + 10^{(2161 - 2296)/400}} = \frac{1}{1 + 10^{-135/400}} \approx \frac{1}{1 + 0.464} \approx 0.683
Probability of losing: 1−0.683=0.3171 - 0.683 = 0.3171 - 0.683 = 0.317
.

Step 2: Adjust for Accuracy
Your accuracy rates (93%, 90%, 91%, 96%, 94%) suggest how well you played relative to an engine’s optimal moves. High accuracy (e.g., 90%+) typically indicates strong play, but it doesn’t guarantee a win, especially against strong opponents. To incorporate accuracy, we can estimate an “effective Elo” for each game by scaling your performance based on accuracy. A rough heuristic is to adjust your Elo downward if accuracy is below a baseline (e.g., 95%) and slightly upward if above.
Let’s assume:
Baseline accuracy = 95% corresponds to your nominal Elo (2296).

For every 1% below 95%, reduce effective Elo by ~20 points (a rough estimate based on typical performance correlations).

For every 1% above 95%, increase effective Elo by ~20 points.

Adjustments:
Game 1: Accuracy = 93% 2% below 95% Effective Elo = 2296−2×20=22562296 - 2 \times 20 = 22562296 - 2 \times 20 = 2256

EA=11+10(2259−2256)/400=11+103/400≈11+1.007≈0.498E_A = \frac{1}{1 + 10^{(2259 - 2256)/400}} = \frac{1}{1 + 10^{3/400}} \approx \frac{1}{1 + 1.007} \approx 0.498E_A = \frac{1}{1 + 10^{(2259 - 2256)/400}} = \frac{1}{1 + 10^{3/400}} \approx \frac{1}{1 + 1.007} \approx 0.498
Loss probability: 1−0.498=0.5021 - 0.498 = 0.5021 - 0.498 = 0.502
.

Game 2: Accuracy = 90% 5% below 95% Effective Elo = 2296−5×20=21962296 - 5 \times 20 = 21962296 - 5 \times 20 = 2196

EA=11+10(2220−2196)/400=11+1024/400≈11+1.148≈0.465E_A = \frac{1}{1 + 10^{(2220 - 2196)/400}} = \frac{1}{1 + 10^{24/400}} \approx \frac{1}{1 + 1.148} \approx 0.465E_A = \frac{1}{1 + 10^{(2220 - 2196)/400}} = \frac{1}{1 + 10^{24/400}} \approx \frac{1}{1 + 1.148} \approx 0.465
Loss probability: 1−0.465=0.5351 - 0.465 = 0.5351 - 0.465 = 0.535
.

Game 3: Accuracy = 91% 4% below 95% Effective Elo = 2296−4×20=22162296 - 4 \times 20 = 22162296 - 4 \times 20 = 2216

EA=11+10(2104−2216)/400=11+10−112/400≈11+0.526≈0.655E_A = \frac{1}{1 + 10^{(2104 - 2216)/400}} = \frac{1}{1 + 10^{-112/400}} \approx \frac{1}{1 + 0.526} \approx 0.655E_A = \frac{1}{1 + 10^{(2104 - 2216)/400}} = \frac{1}{1 + 10^{-112/400}} \approx \frac{1}{1 + 0.526} \approx 0.655
Loss probability: 1−0.655=0.3451 - 0.655 = 0.3451 - 0.655 = 0.345
.

Game 4: Accuracy = 96% 1% above 95% Effective Elo = 2296+1×20=23162296 + 1 \times 20 = 23162296 + 1 \times 20 = 2316

EA=11+10(2260−2316)/400=11+10−56/400≈11+0.724≈0.580E_A = \frac{1}{1 + 10^{(2260 - 2316)/400}} = \frac{1}{1 + 10^{-56/400}} \approx \frac{1}{1 + 0.724} \approx 0.580E_A = \frac{1}{1 + 10^{(2260 - 2316)/400}} = \frac{1}{1 + 10^{-56/400}} \approx \frac{1}{1 + 0.724} \approx 0.580
Loss probability: 1−0.580=0.4201 - 0.580 = 0.4201 - 0.580 = 0.420
.

Game 5: Accuracy = 94% 1% below 95% Effective Elo = 2296−1×20=22762296 - 1 \times 20 = 22762296 - 1 \times 20 = 2276

EA=11+10(2161−2276)/400=11+10−115/400≈11+0.514≈0.660E_A = \frac{1}{1 + 10^{(2161 - 2276)/400}} = \frac{1}{1 + 10^{-115/400}} \approx \frac{1}{1 + 0.514} \approx 0.660E_A = \frac{1}{1 + 10^{(2161 - 2276)/400}} = \frac{1}{1 + 10^{-115/400}} \approx \frac{1}{1 + 0.514} \approx 0.660
Loss probability: 1−0.660=0.3401 - 0.660 = 0.3401 - 0.660 = 0.340
.

Step 3: Probability of Losing All Five Games
Assuming independence, the probability of losing all five games is the product of the individual loss probabilities:
P(all losses)=P(loss1)×P(loss2)×P(loss3)×P(loss4)×P(loss5)P(\text{all losses}) = P(\text{loss}_1) \times P(\text{loss}_2) \times P(\text{loss}_3) \times P(\text{loss}_4) \times P(\text{loss}_5)P(\text{all losses}) = P(\text{loss}_1) \times P(\text{loss}_2) \times P(\text{loss}_3) \times P(\text{loss}_4) \times P(\text{loss}_5)
P=0.502×0.535×0.345×0.420×0.340P = 0.502 \times 0.535 \times 0.345 \times 0.420 \times 0.340P = 0.502 \times 0.535 \times 0.345 \times 0.420 \times 0.340
Calculate step-by-step:
0.502×0.535≈0.268570.502 \times 0.535 \approx 0.268570.502 \times 0.535 \approx 0.26857

0.26857×0.345≈0.09265650.26857 \times 0.345 \approx 0.09265650.26857 \times 0.345 \approx 0.0926565

0.0926565×0.420≈0.03891570.0926565 \times 0.420 \approx 0.03891570.0926565 \times 0.420 \approx 0.0389157

0.0389157×0.340≈0.01323130.0389157 \times 0.340 \approx 0.01323130.0389157 \times 0.340 \approx 0.0132313

I don’t think anybody that is human can read that. Why are you posting this? And why here? I think this should be in Game Analysis, if it should be anywhere at all.

The chances might be 0% with that 96% accuracy

After refining the question here is the answer for question 2 from the AI

The fact that Player 1 (2296) lost all five games despite being higher-rated than most opponents (expected score ~3/5 based on rating differences) and the opponents’ high accuracies suggests either exceptional performance by the opponents or underperformance by Player 1.
Answer for Question 2:
The odds of all five opponents achieving accuracies of 93%, 90%, 91%, 96%, and 95% in games over 40 moves are approximately 1 in 132,000 (0.0007573%), assuming independent performances and a normal distribution of accuracy with a standard deviation of 6%.
Final Answer
Expected accuracy rates:
2259: ~85-88%

2220: ~84-87%

2104: ~82-85%

2260: ~85-88%

2161: ~83-86%

Odds of observed accuracies: Approximately 1 in 132,000 (0.0007573%).

Interesting!

If the length of the game and accuracy of you your own moves from computer evaluation is included the odds actually increase which is surprising

Step 5: Contextual Analysis
Player 1’s performance: Their accuracies (84%, 88%, 79%, 75%, 87%; average ~82.6%) are below the expected ~87.5% for a 2296-rated player. Notably, the 75% accuracy in the 19-move game (vs. 2220, 96% accuracy) suggests a significant mistake, likely leading to an early loss and inflating the opponent’s accuracy. The 88% and 87% accuracies in the 27-move and 71-move games are closer to expected but still low for a 2296-rated player, contributing to losses.

Game lengths:
Short games (19, 22, 27 moves): High opponent accuracies (90%, 91%, 96%) are more plausible due to fewer moves and potential blunders by Player 1 (e.g., 75% in the 19-move game).

Medium game (37 moves): 93% accuracy for a 2161-rated player is high but feasible if Player 1’s 84% included exploitable errors.

Long game (71 moves): 95% accuracy for a 2259-rated player is exceptional, as long games typically see more inaccuracies. Player 1’s 87% suggests a competitive game, but the opponent played nearly flawlessly.

The high opponent accuracies and Player 1’s losses (0/5, despite an expected score of ~3/5 based on rating differences) suggest either exceptional opponent performance or factors like strong preparation, simplified positions due to Player 1’s errors, or, in online settings, potential external assistance (though not implied).
Answer for Question 2:
The odds of the opponents achieving accuracies of 93%, 90%, 91%, 96%, and 95% in games of 37, 27, 22, 19, and 71 moves are approximately 1 in 393,000 (0.0002545%).
Final Answer
Expected accuracy rates:
2161: ~83-86%

2260: ~85-88%

2104: ~82-85%

2220: ~84-87%

2259: ~85-88%

Odds of observed accuracies: ~1 in 393,000 (0.0002545%).

The assesment by the AI of the standard of chess is quite reasonable

Losses Against Lower-Rated Opponents:
Player 1, rated 2296, should have an edge over opponents rated 2104-2260. The Elo formula predicts a score of ~0.6 against 2161, ~0.53 against 2260, ~0.67 against 2104, ~0.56 against 2220, and ~0.53 against 2259, totaling ~2.9-3.1/5. Losing all 5 games is statistically unlikely (probability <1%) and indicates Player 1 failed to capitalize on their skill advantage.

Opponents’ Exceptionally High Accuracies:
The opponents’ accuracies (90-96%) are well above their expected ranges (82-88%). This suggests Player 1’s mistakes created simplified or winning positions, making it easier for opponents to play accurately. For instance, a blunder by Player 1 could lead to a position where the opponent’s best moves are straightforward, inflating their accuracy.

Game Length Patterns:
Short games (19, 22, 27 moves): These losses, especially the 19-move game with 75% accuracy, point to early blunders or tactical oversights, allowing opponents to win quickly with high accuracy.

Medium game (37 moves): The 84% accuracy is below Player 1’s expected level, suggesting inaccuracies that the 2161-rated opponent (93%) exploited.

Long game (71 moves): The 87% accuracy is closer to expected, but the 2259-rated opponent’s 95% accuracy indicates they played exceptionally well, possibly capitalizing on a late-game error by Player 1.

The "AI" generated content in your first comment made at least some sense. What you copy now is absolutely useless and getting more and more ridiculous. But you apparently trust those tools and ignore everything other users tried to explain so why do I even bother?

@mkubecek

I'm also by now completely confused as to what question the OP wants to answer. The opening post was about the probability of a 5-game losing streak, but then he said that's not the actual question he's interested in and he wants to create some kind of performance metric.

One thing is for sure though, LLMs are incompetent at playing chess, so why would you trust them with creating a useful metric to analyse games? (;