MrGoodFlop
Rock Star
Silver Level
I found an article on Wikkipedia that gives hand ranking according to expected value.
I think it should provide some interesting statistics to add to the discussion.
It gave me the idea to do the analysis that follows.
This is the link: Texas hold 'em starting hands - Wikipedia, the free encyclopedia
I reproduced one of the tables here:
Tier.. hands......................................... EV
1..... AA, KK, QQ, JJ, AKs........................ 2.32 - 0.78
2..... AQs, TT, AK, AJs, KQs, 99............... 0.59 - 0.38
3..... ATs, AQ, KJs, 88, KTs, QJs.............. 0.32 - 0.20
4..... A9s, AJ, QTs, KQ, 77, JTs............... 0.19 - 0.15
5..... A8s, K9s, AT, A5s, A7s................... 0.10 - 0.08
6..... KJ, 66, T9s, A4s, Q9s..................... 0.08 - 0.05
7..... J9s, QJ, A6s, 55, A3s, K8s, KT......... 0.04 - 0.01
8..... 98s, T8s, K7s, A2s......................... 0.00
9..... 87S, QT, Q8s, 44, A9, J8s, 76s, JT... (-) 0.02 - 0.03
It shows how hands have been grouped according to expected value.
The grouping was determined from statistics taken from actual play of a large number of hands.
What is interesting to note is the number of hands in each tier.
5 in the first, 6 in the second, etc...
The table only shows 52 hands.
Since we know there are 169 possible 2 card hands in Texas Hold'em
then we can add another row to the table, tier 10, showing the remaining 117 hands that have an EV less than -0.03.
If during a game, the hole cards are dealt randomly, we should expect, on average, to be dealt 5 hands from tier 1 for every 169 hands we have been dealt.
Similarly, we should be dealt 6 hands from tier 2, 6 from tier 3, etc...
The following table to shows that.
tier # hands in tier
1..... 5
2..... 6
3..... 6
4..... 6
5..... 5
6..... 5
7..... 7
8..... 4
9..... 8
10....117
total 169
Now, ideally, when we play a game, we would like all our pocket cards to be from lower tier numbers since these are the cards that statistically win most hands.
However we can see from the table that we are going to be getting most of our pocket cards from tier 10 and that they are most likely going to be losing hands.
I have over 10,000 hands recorded in my Poker Tracker database and I wanted to see how the hand distribution compares to the above tables.
I exported the hand data in a spreadsheet and came up with a set of charts.
One chart for the poker stars hands and one for the FullTilt hands.
The charts show that in general, I am being dealt more hands than expected from tier 10 and less hands than expected from tiers 1 to 9.
Here are some of the numbers for the pokerstars hands.
The numbers from the FullTilt hands are similar.
tier times_dealt..... expected # hands..... variance
1.......... 178............... 244......................... -0.80%
2.......... 217............... 293......................... -0.92%
3.......... 247............... 293......................... -0.55%
4.......... 256............... 293......................... -0.45%
5.......... 187............... 244......................... -0.69%
6.......... 179............... 244......................... -0.79%
7.......... 277............... 342......................... -0.78%
8.......... 95................ 195.......................... -1.21%
9.......... 360............... 390......................... -0.37%
10........ 6249............. 5708........................ 6.56%
total..... 8245............. 8245........................ 0.00%
Unfortunatelly I can't figure out how to insert the chart images in the post.
If someone can explain how to do it I will post them.
Does that indicate that these hands were not dealt randomly?
If the hands were dealt randomly, all the variance numbers should be close to zero and about half of them should be positive.
Why is there such a significant skew towards the negative EV hands?
I made the same analysis using only the hands from a tournament were I did well (placed 3rd).
It clearly shows that during that tournament, I was dealt more cards from the positive EV tiers and less from the negative EV tiers.
Of course, as a result, I was playing more hands and winning more hands than usual.
tier....... times_dealt... expected # hands....... variance
1.......... 7................. 9............................. -0.71%
2.......... 15.............. 11............................. 1.27%
3.......... 14.............. 11............................. 0.95%
4.......... 10.............. 11............................. -0.33%
5.......... 9................. 9............................. -0.06%
6.......... 4................. 9............................. -1.67%
7.......... 9................ 13............................. -1.25%
8.......... 3................. 7............................. -1.40%
9.......... 17............... 15............................. 0.73%
10........ 223............ 215............................. 2.47%
total..... 311............ 311............................. 0.00%
Here the variance is not as skewed towards the negative EV tier.
There is some positive variance for tiers 2 and 3.
The number of hands in tier 10 is closer to what is expected.
I think this shows a lot more than you would see just by looking at the single AA hand.
If anyone else wants to do that exercise, I can provide the Excell spreadsheet if someone explains how to post it.
I think it should provide some interesting statistics to add to the discussion.
It gave me the idea to do the analysis that follows.
This is the link: Texas hold 'em starting hands - Wikipedia, the free encyclopedia
I reproduced one of the tables here:
Tier.. hands......................................... EV
1..... AA, KK, QQ, JJ, AKs........................ 2.32 - 0.78
2..... AQs, TT, AK, AJs, KQs, 99............... 0.59 - 0.38
3..... ATs, AQ, KJs, 88, KTs, QJs.............. 0.32 - 0.20
4..... A9s, AJ, QTs, KQ, 77, JTs............... 0.19 - 0.15
5..... A8s, K9s, AT, A5s, A7s................... 0.10 - 0.08
6..... KJ, 66, T9s, A4s, Q9s..................... 0.08 - 0.05
7..... J9s, QJ, A6s, 55, A3s, K8s, KT......... 0.04 - 0.01
8..... 98s, T8s, K7s, A2s......................... 0.00
9..... 87S, QT, Q8s, 44, A9, J8s, 76s, JT... (-) 0.02 - 0.03
It shows how hands have been grouped according to expected value.
The grouping was determined from statistics taken from actual play of a large number of hands.
What is interesting to note is the number of hands in each tier.
5 in the first, 6 in the second, etc...
The table only shows 52 hands.
Since we know there are 169 possible 2 card hands in Texas Hold'em
then we can add another row to the table, tier 10, showing the remaining 117 hands that have an EV less than -0.03.
If during a game, the hole cards are dealt randomly, we should expect, on average, to be dealt 5 hands from tier 1 for every 169 hands we have been dealt.
Similarly, we should be dealt 6 hands from tier 2, 6 from tier 3, etc...
The following table to shows that.
tier # hands in tier
1..... 5
2..... 6
3..... 6
4..... 6
5..... 5
6..... 5
7..... 7
8..... 4
9..... 8
10....117
total 169
Now, ideally, when we play a game, we would like all our pocket cards to be from lower tier numbers since these are the cards that statistically win most hands.
However we can see from the table that we are going to be getting most of our pocket cards from tier 10 and that they are most likely going to be losing hands.
I have over 10,000 hands recorded in my Poker Tracker database and I wanted to see how the hand distribution compares to the above tables.
I exported the hand data in a spreadsheet and came up with a set of charts.
One chart for the poker stars hands and one for the FullTilt hands.
The charts show that in general, I am being dealt more hands than expected from tier 10 and less hands than expected from tiers 1 to 9.
Here are some of the numbers for the pokerstars hands.
The numbers from the FullTilt hands are similar.
tier times_dealt..... expected # hands..... variance
1.......... 178............... 244......................... -0.80%
2.......... 217............... 293......................... -0.92%
3.......... 247............... 293......................... -0.55%
4.......... 256............... 293......................... -0.45%
5.......... 187............... 244......................... -0.69%
6.......... 179............... 244......................... -0.79%
7.......... 277............... 342......................... -0.78%
8.......... 95................ 195.......................... -1.21%
9.......... 360............... 390......................... -0.37%
10........ 6249............. 5708........................ 6.56%
total..... 8245............. 8245........................ 0.00%
Unfortunatelly I can't figure out how to insert the chart images in the post.
If someone can explain how to do it I will post them.
Does that indicate that these hands were not dealt randomly?
If the hands were dealt randomly, all the variance numbers should be close to zero and about half of them should be positive.
Why is there such a significant skew towards the negative EV hands?
I made the same analysis using only the hands from a tournament were I did well (placed 3rd).
It clearly shows that during that tournament, I was dealt more cards from the positive EV tiers and less from the negative EV tiers.
Of course, as a result, I was playing more hands and winning more hands than usual.
tier....... times_dealt... expected # hands....... variance
1.......... 7................. 9............................. -0.71%
2.......... 15.............. 11............................. 1.27%
3.......... 14.............. 11............................. 0.95%
4.......... 10.............. 11............................. -0.33%
5.......... 9................. 9............................. -0.06%
6.......... 4................. 9............................. -1.67%
7.......... 9................ 13............................. -1.25%
8.......... 3................. 7............................. -1.40%
9.......... 17............... 15............................. 0.73%
10........ 223............ 215............................. 2.47%
total..... 311............ 311............................. 0.00%
Here the variance is not as skewed towards the negative EV tier.
There is some positive variance for tiers 2 and 3.
The number of hands in tier 10 is closer to what is expected.
I think this shows a lot more than you would see just by looking at the single AA hand.
If anyone else wants to do that exercise, I can provide the Excell spreadsheet if someone explains how to post it.
