# equity issue with equity calculator software

sorry for what is likely a straightforward question but when using equilab I see the following:

my hand: 8♥8⋄

board (flop+turn): 6♥8♣Q♣K⋄

If I calculate the equity of my hand versus:

• A♣9♣ it is (me/villain): +/- 84/16
• K♣J♣ it is (me/villain): +/- 82/18

since I can only be beaten by a flush both hands have the same number of outs so why is the equity different?

• How did you end up with this `84/16` equity? I understand the `82/18` though. Can you make it clear in the question?
– user1165
Commented Aug 3, 2015 at 21:27
• Just looked at this quickly so correct me if I'm wrong but doesn't A9 give you 8 outs (A234579T) while KJ gives 7?? (23457TJ) Commented Aug 5, 2015 at 10:17

I ran a simulation of around 5K hands and i found the following:

## 88 vs A9s (84% to win)

• Four of a Kind, won 128 times (3%)
• Full House, won 999 times `(20%) <---`
• Three of a Kind, won 3113 times (62%)

## 88 vs KJs (82% to win)

• Four of a Kind, won 116 times (2%)
• Full House, won 900 times `(18%) <---`
• Three of a Kind, won 3125 times (63%)

I think the "issue" lies to the fact that a `K` on the board and a `K` on villain's hole cards reduces the ability for the `88` to hit as many full houses against `KJ` than against `A9` (only 2 kings left).

## EDIT

Once again, i upped the sample size to confirm if there are any gaps due to small size above:

## 88 vs KJs (81% to win, 500k hands)

• Four of a Kind, won 11334 times (2%)
• Full House, won 90622 times (18%)
• Three of a Kind, won 306948 times (61%)

## 88 vs A9s (84% to win, 500k hands)

• Four of a Kind, won 11302 times (2%)
• Full House, won 101518 times (20%)
• Three of a Kind, won 307754 times (62%)

## 88 vs KJs (81% to win, 5m hands)

• Four of a Kind, won 112983 times (2%)
• Full House, won 909900 times (18%)
• Three of a Kind, won 3069012 times (61%)

## 88 vs A9s (84% to win, 5m hands)

• Four of a Kind, won 113070 times (2%)
• Full House, won 1024030 times (20%)
• Three of a Kind, won 3068647 times (61%)

I may be wrong or my code may be wrong, though the statistics are not lying; the `88 vs A9s` hits around +2 % more full houses than `88 vs KJs`. Additionally, if the `KJ` hits trips, we will hit full houses then.

• vlzvl that sounds like the correct answer. I did not think of that, thx! May I ask what software you used for your simulations?
– roel
Commented Aug 4, 2015 at 15:24
• This is wrong. The hands are 100% equivalent, and a 5000-hand simulation is just going to produce a big margin of error. Yes, against the KJ we will hit fewer full houses, but he will win with trips by exactly that same number of times more. Simulations are nice, but actual accurate math is better. Commented Aug 4, 2015 at 19:25
• Hi Lee, it is not wrong. It is maybe not perfectly explained but he is right. In the K/J hand the villain has 8 outs while in the A/9 hand the villain has 7 outs (he loses one extra out - the Kc since that would make a full house - next to the 6c).
– roel
Commented Aug 4, 2015 at 20:56
• @roel, this is a custom app, using Cactus Kev evaluator
– user1165
Commented Aug 5, 2015 at 0:18
• @roel, I edited the answer as well
– user1165
Commented Aug 5, 2015 at 0:19

The hands are not equivalent. A flush beats trips but a boat beats a flush. The 88 can make a boat with a 6 or K. So the 6 or K on the BOARD are dead for both flush draws. Since one hand holds the K then it is not dead as it is not on the board.

52-8 = 44 cards out

On the A9 neither the 6 or K is good so there are 7 outs.
23457TJ
(44-7)/44 = 84.09%

On the KJ only the 6 is not good so the are 8 outs.
234579TA
(44-8)/44 = 81.18%

6K of clubs would have no flush block and pick up 2 outs to an over boat for 11 outs.