Shared betting profitability

I was recently playing blackjack in a casino and went on a big run. One of the big parts of this run was that another gentleman at the table was offering to share his action whenever he had a hand to double with.

For example, if he was showing an 11 (against a dealer 5) and had a $400 bet out, he'd double down by putting up $200 himself and I could put up the other $200. If he won, I'd get $400 back.

Intuitively, it seems like this would be hugely beneficial to me. Possibly to the point of making the table +EV to play on with just basic strategy. Does anyone know if that's mathematically provable though?

Assuming these rules:
- I was betting the minimum each time: $50
- He was betting $400 each hand and would let me put in $200 on any split/double of his (and get back $400 on the win)
- Assume we are both playing perfect basic strategy but not counting
- Dealer hits soft 17, double down after splitting, late surrender, resplit aces, 6 decks, blackjack pays 3-2

There's a list of EVs here - https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/
For instance you can see that doubling 11 vs 5 is very good (although the figure given there isn't exactly your rules, you can get the idea). Technically then you can look at all the doubles and add up the probabilities of it happening.

Quote: veritasio

For example, if he was showing an 11 (against a dealer 5) and had a $400 bet out, he'd double down by putting up $200 himself and I could put up the other $200. If he won, I'd get $400 back.

Intuitively, it seems like this would be hugely beneficial to me. Possibly to the point of making the table +EV to play on with just basic strategy. Does anyone know if that's mathematically provable though?

You're right. If he's offering to let you share in the action on double downs, that can be hugely +EV, It is mathematically provable and your edge could be calculated. Without doing the calcs, intuitively I'd say the situation you described was +EV and I'd have jumped at the opportunity.
I guess his motivation for offering the action would be to limit the volatility in his session, which you are taking onto yourself.

Quote: veritasio

I was recently playing blackjack in a casino and went on a big run. One of the big parts of this run was that another gentleman at the table was offering to share his action whenever he had a hand to double with.

For example, if he was showing an 11 (against a dealer 5) and had a $400 bet out, he'd double down by putting up $200 himself and I could put up the other $200. If he won, I'd get $400 back.

Intuitively, it seems like this would be hugely beneficial to me. Possibly to the point of making the table +EV to play on with just basic strategy. Does anyone know if that's mathematically provable though?

Assuming these rules:
- I was betting the minimum each time: $50
- He was betting $400 each hand and would let me put in $200 on any split/double of his (and get back $400 on the win)
- Assume we are both playing perfect basic strategy but not counting
- Dealer hits soft 17, double down after splitting, late surrender, resplit aces, 6 decks, blackjack pays 3-2

I find the infinite-deck model for your rules gives you an EV of at least 14.2% (based on your initial bet) minus the house edge of your main bet.

You would be betting $200 on all his basic strategy double-downs. And you would be betting $200 on his positive EV splits and re-splits. You would not do the following negative EV basic strategy splits: 9s vs 9, 8s vs 8-A, 7s vs 2-3 & 7, 6s vs 2-4, 3s vs 2-3 & 7, and 2s vs 2-3.

Your advantage would be above 14.2% if he did the negative EV splits for the full $400 and you did $200 on any double-downs resulting from those splits.

Also, if he offers to split and re-split10s, you should take that offer against any card.