What would you do?

Summary of situation: You and one other player left with one advancing. Last hand. You bet and act first. Your bet covers high and low. (If you want to check, I'll provide numbers, but that's not really the question.) You get a 15. Other player gets 13 to dealer 8. Do you hit or stand?

 

Ok my 10 second answer is to hit. In a situation like this if you have both the high and low, you want the same outcome as your opponent. With 13 against 8, he is more likely to hit than stand and hence my choice of hitting. If you bust, then he may be likely to stay and in this case he will be more than 50% likely to lose and you advance. If you chose to stay, he will have no choice but to hit and will have 38% chance of having 17-21 (better hand than yours).

 

This is a case where knowing your opponent is key. These are my 1 minute answers:
If you think he is a basic strategy player, then he will hit and my gut says to hit as well.
If you think that he will double no matter what you do, then you can also double and retain both the high and low, which is what I would do.
If your double will give up the low and he knows it, then don't do that. Hit instead.
If, for some reason, you know that he will stand then

 

Thanks Pro and gron. I hit, busted. He hit to 20 and dealer busted.

 

[Edit --- this response is incorrect -- see below for the correct response and sim results ]
Some sim results. You should hit regardless of whether your opponent is a basic strategy player or a tournament expert, but it's close in either situation.

If your opponent is a basic strategy player, then you should hit to 16 for a 74.3% chance of advancing vs 73.5% for standing and 30.8% for doubling.
If your opponent will respond optimally, then you should hit to 18 for a 65.4% chance of advancing vs 65.2% for standing and 28.7% for doubling.

 

Interesting. Wong's Table 5 says hit to 17.

 

After seeing Colin's response and considering how close the sim results were, I decided that I may not have run enough iterations for the sims. I re-ran the sims for approximately 1.5 billion iterations this time. The results did change, and Wong is correct, but the decision is still very close.

If your opponent is a basic strategy player, then you should stand on your 15 for a 74.49% chance of advancing vs 74.46% for hitting and 30.48% for doubling.
If your opponent will respond optimally, then you should hit to 17 for a 65.21% chance of advancing vs 64.60% for standing and 30.26 for doubling.

Sorry for any confusion. I'll try not to be so eager that I post incomplete results next time.

 

Given the closeness, I think you should be forgiven.

It makes me wonder how close many of the decisions might be. If table 5 were to be recast as a list of variations from BS, ordered by their percentage impact, then there might be scope to learn just the top few; a bit like the Illustrious 18, etc. in card counting.

 

That's something I could probably put together.

 

It's not something I have a burning need for myself; my interest is very much academic. (It's been quite a while since I had the opportunity to play in a BJ tournament, sadly.)

So I'd say you should only take on the task if it's something you want to do to satisfy your own curiosity (rather than mine).