So... Pretty sure this is the first time I've had to ask a stupid question here, and it's a tad embarrassing.

Say a guy had a super-mega-infinite ram desktop that could design and launch a Russian space shuttle. Then one day that computer went down in flames. Now our hero is forced to use primitive technology complete with a missing "u" button on the keyboard. Current device probably cannot even load the website to download a solver. OTTH:

If one were using Equilab (flopzilla hasn't been invented yet), how would someone go about calculating range v range equity against a range that included partials (like Villain is expected to play 78s 70% of the time)?

Looking for "by hand method" not equilab hack.

Thanks.

I warn you, this is NOT a trivial calculation.

If both ranges have mixed hands, you'd have to manually calculate the equity for every combo vs every other combo in the range, calculate the probability for each matchup based on weighting and card removal. This is the only way to guarantee that you've correctly accounted for card removal. For a full range with mixed weights pre you'd be looking at 169*169= 28561 individual calculations.

If only ONE range has mixed hands, you could do this a lot faster by calculating each hand's equity vs the other player's entire (no mixing) range. Manually calculate each hand, one at a time, then apply weighting based on how many combinations are in that hand class and what % of that hand is present in the range. I'm not sure this method fully accounts for card removal though.

Either that or just use suit-select to split the weights as needed. There may be some free online calculators capable of calculating mixed weights as well.

I see where you're going, but would you not be able to just apply a weight function?

Say you ran equilab against two ranges, and the first time with the partials at 100%, then running the non-mix range against the 100% (soon to be partials)... I'm not explaining that right.

So Hero's rfi range is static and doesn't involve any partials. Villain's calling range includes a mostly static range--but 30% of the time he's going to call with 78s.

If you ran equilab with villain's entire range with 78s at 100%, then just 78s vs Hero... would you be able to weight the result similar to the method used for political surveys?

If there's only one mixed hand that approximation probably works fine. But how would you approach it if you had something like 5 mixed hands in the range?

The complicated part is that simply weighing them together based on raw combos/frequency isn't quite right as it ignores card removal.

A naive approach is something like well I have "XYo half the time, so I will weigh it as 6 combinations". But in reality, your chances of getting XYo are affected by the opponent's range. Hell they are even affected by ranges not even in the hand (see bunching effect), but we have to draw a line somewhere for the sake of simplicity.

Probably just replace the space computer then. Thanks for giving me perspective though, really stuck there for a bit.

Let's say you have range A of AcAd(50%) KsKd(50%) AcQd(50%) so in total 1.5 combos and some other range B. You calculate equity like this

0.5/(1.5)*(equity of AcAd vs range B)+0.5/(1.5)*(equity of KsKd vs range B)+0.5/(1.5)*(equity of AcQd vs range B)


If range B has mixed combos you add combo v combo equities in same way.

This would ignore the card removal effects e.g. how often you have each of those mixed hands with respect to villain's range, no?

Actually you probably should weighted probabilities bit differently because othere range can have more/less combos depending on which hand you calculate equity against, but it's small thing unless ranges are super narrow. That effect you have even without ranges with mix strategies.