Stud hi lo last card

The 4th street raise isn’t a classic iso-raise — but mathematically, it’s much closer to break-even (and potentially slightly +EV) than people assume.

Compute distributions for hand: 4d5c7c8c Dead cards are: 9h5hJdJs2d7d conducting 10000000 runs...........

Qualifying low: 74.52%

High hand distribution
======================
STRAIGHT_FLUSH 0.69% cumulated: 0.69%
POKER 0.02% cumulated: 0.71%
FULL HOUSE 0.50% cumulated: 1.22%
FLUSH 12.88% cumulated: 14.09%
STRAIGHT 23.25% cumulated: 37.34%
SET 2.00% cumulated: 39.34%
TWO PAIR 12.11% cumulated: 51.45%
ONE PAIR 32.65% cumulated: 84.10%
HIGH_CARD 15.90% cumulated: 100.00%

Lows
===============
5-high: 0.42%
6-high: 1.40%
7-high: 21.80%
8-high: 50.90% - all 8-lows are 87 lows

The gutshot and the lifeliness of Clubs help Hero's final hands to be at least a straight >37%.
But the deciding factor in this hand is his low equity.

If we put both villains on tight ranges:

- Villain2 starting with QQ,KK, split J, three suited cards or perfect rundowns(+/-suited)
- Villain on a better low draw and/or a low draw + 3/4-Flush and/or 3-Straight

Hero's range equity is ~30.0%. (Fix 10.000 hand combos where villains fall into the above ranges, then conduct 10.000 Monte-Carlo/board runs and average equity)
However, if we make Villain's range wider so that it now also contains 3-Lows + one pair, Hero's low equity increases considerably, bringing the total range equity to

~34.8%

slightly above the +EV threshold for this bet (33.3%)

A flat call remains standard, but the raise isn’t nearly as bad as described.
Hero has one more thing going for him: guaranteed absolute position on 5th street!
If he catches a scary card - basically any non-4/5 low card - it is likely getting checked to him and he can decide the course.

As for 7th — yes, absolutely a call. After Villain2 checks 6th street, Hero has a good chance to either have the best high or low hand in the side pot. Plus, if Villain2 does hat have a low, we also win half of the main pot.

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