Protecting a Large Lead

True -- and sometimes that's exactly the case!!

 

Back to the question of what should BR2 do with his 16 vs 6 if we had both bet max and I stood on my 15 ....

It is worth pointing out that the one thing he should not to is to stand. That would give me a lock. This kind of lock comes up often when you're playing against basic strategy players and is worth keeping an eye out for when you act after your opponent.

That leaves his options as hitting (but to what total?) in order to create a swing or doubling to take the high.

Chairman correctly reasoned that, if he hits, he should hit only only once for a 14.35% chance of success.
However, if he doubles, as The Professional suggests, he has 31.20% chance of success.

This illustrates a rule of thumb that I use, which is that, given a choice of doubling for the high or trying to create a swing by hitting, doubling is almost always the superior play. Even with BR2 holding a high-ish bustable hand, and our opponent standing stiff, as in this case, doubling is more than twice as successful as hitting. Furthermore, doubling would still be superior with these totals regardless of the dealer's up card.

What if BR2 had 17 instead of 16? Doubling is still the superior play except vs a dealer 7 against which he should stand and hope for a push. Doubling would still be superior to hitting, however.

Once BR2 has 18 or more, then standing is the best play for all dealer up cards. However doubling still remains superior to hitting even for a total of 20. Why? (because the sim says so!, but logically ...). Because when doubling, BR2 needs only survive the hit and win his hand, or push i t while BR1 loses in order to succeed. When hitting, he must accomplish all of that and BR1 has to lose when he wins in order for him to be successful.