I think you have several errors. I believe the weights are roughly 60/40 for 78 vs Pairs case if you assume the number of combos as the weighting factors (16 vs 12). Also, your calc 2.13/4 is a bit off. Equilab shows the actual equity is 50%. Nevertheless, I would think very few players can do this calc on line or live and have to rely on an equity calculator or crude guess so I am impressed that you did this calc while playing.
For estimating equity, here are some ways to do so actively:
Outs (4x 2x rule), standard confrontations (e.g. high pair vs low pair is 80:20), memorize selected hand vs range cases and simple combo analysis (as you did for a limited opponent range). When I used outs for your example with the different weights, I got 46% as an estimate of the Turn equity.
The following table is an example of Pairs vs Opponent Range where I rounded the exact values. Add or subtract a few percentage points for in-between values.
| | Approximate | SD Equity | Estimates | |
| | .........Villain | Range Top | X%........ | |
| Pair | 5% | 10% | 20% | 30% |
| 44 | 30% | 40% | 45% | 50% |
| 88 | 35% | 45% | 50% | 55% |
| QQ | 60% | 65% | 70% | 75% |
Example: 88 vs a top 20% range has showdown equity of about 50%.
Here’s another approach. Instead of estimating equity, which is hard, much easier is calculating the equity you need to make a bet or call. For example, the pot odds are “on the table” and the equity you need is 1/(1+Pot Odds), a relatively easy calc. Then you can make a decision based on how well you think your equity meets that need without having to estimate it quantitatively.
