Win Both Ways vs. multiple opponents, acting first

Final hand of a BJ semifinal round, only 3 people left. I am BR1 with about 27k, BR2 has 20k and BR3 has 17k. Secret bet, I bet enough to cover double-up by BR2 and they both go all-in, so I have high and low covered but cannot survive a half-swing by either (i.e., push vs. loss, push vs. win, etc.).

Dealer gets a face card, I have 13, BR3 (acting second) gets 14, BR2 gets 15. I hit and get a 4 to 17. What's my next move?

 

Stand

I would have stood on the 13. Since you go lucky, you certainly do not need to hit again.

 

Wong Table

Looking at Wong's table 5, if BR1 wins both ways and plays first, then BR1 should hit to 15 against dealer 10 when BR2 has 12-16. I do not know what you should do with multiple people. However, with 2 people having a shot hitting the stiff hand, I would imagine, if anything, that you might contemplate hitting higher than 15.

Larry

 

I had my simulator generate the optimal playing strategy for this situation

BR1: Bankroll: 27000, Bet: 13100
BR3: Bankroll:17000, Bet 17000
BR2: Bankroll: 20000, Bet 20000

with 4 variations:

1) All players play optimally (generates optimal strategy for BR1 vs optimal response strategies for BR2 and BR3)
2) BR2 (player 3) plays basic strategy, BR3 (player 2) plays optimally.
3) BR2 plays optimally, BR3 plays basic strategy
4) BR2 and BR3 both play basic strategy.

I also ran these scenarios with late surrender allowed (since BR1's surrender beats a push by the other players) and no surrender allowed.

The answer to the question of "What's my next move?" in all situations was "Stand on your 17" by a margin of between 3% and 5%.

But how about the question of what to do initially (after the first two cards)? In all cases except 1, the answer was to hit the 13 (although the decision was extremely close: <= 1% in all cases) and to stand on 14 or better. The one exception was case 2 with surrender for which the recommendation was to stand on 13. Even then the numbers were close enough that perhaps more iterations would swing the decision:

Searching for state *{*13}{14}{15} vs T
Hand Strategy
Stand == 26192115.0000/32791914 == 0.7987
Hit == 26143464.0000/32791914 == 0.7973
Surrender == 5127704.0000/6707615 == 0.7645
Double (1/2 - 2/2) == 2015901.0000/6707615 == 0.3005

Note that doubling here is much worse than hitting since it gives up the low to BR2's basic strategy surrender (15 vs 10).

Here is an example of the output for variation 1 with surrender available so you can get an idea of what my generator can do:

View attachment both-perfect-with-surrender.txt

Notes:
- The results for hands 14 and higher show only hit and stand, since these hands resulted from hitting the initial 13.
- The simulated result for player 1 is slightly better than the computed result for hitting 13 because the computed result is based on analyzing playing decisions, which means that the dealer did not have blackjack under his 10. The simulated result includes the case where the dealer has black jack, in which case player 1 finishes first. So, the simulated result represents the probability of success before the dealer checks for black jack and the computed result represents the probability of success after the dealer checks (and does not have black jack). I find it useful to be able to obtain both figures.

 

Do you know where I can dl the simulator you used?

 

MonkeySystem is correct. I've spent years creating my software and, while I do hope to make it available someday, it's not ready for public use yet. Mainly because it has no GUI and the command line interface is so cryptic that even I need to read the code sometimes to come up with the right incantation! Also, right now it only runs on Linux.

I have, however, worked with people to solve problems or find answers to questions they have using my software. If you have something in particular that you want to find out, PM me.