hjuosh
Visionary
Platinum Level
I was dealt pocket eights three times in a row on GGPOKER 🫨 So I asked AI about the probabilities. Here’s the answer.
Very, very rare.
• Probability of being dealt 88 in one hand: there are \binom{52}{2}=1326 possible combinations and \binom{4}{2}=6 ways to make pocket eights, so 6/1326 = 1/221 \approx 0.452\%.
• Three consecutive hands with 88 (with the deck shuffled each time):
(1/221)^3 = 1/10,793,861 \approx 9.26\times10^{-8}, or 0.00000926%, about one in 10.8 million.
For comparison, “any pocket pair” three times in a row would be (1/17)^3 \approx 1/4,913 (~0.020%)
As a comment. I went all-in each time... and won all three!
Very, very rare.
• Probability of being dealt 88 in one hand: there are \binom{52}{2}=1326 possible combinations and \binom{4}{2}=6 ways to make pocket eights, so 6/1326 = 1/221 \approx 0.452\%.
• Three consecutive hands with 88 (with the deck shuffled each time):
(1/221)^3 = 1/10,793,861 \approx 9.26\times10^{-8}, or 0.00000926%, about one in 10.8 million.
For comparison, “any pocket pair” three times in a row would be (1/17)^3 \approx 1/4,913 (~0.020%)
As a comment. I went all-in each time... and won all three!
