Final Hand. Min/Max bet 100/1000 and surrender allowed. BR1 3101 chips first to act and BR2 2600 chips. -I would like to know the outcome for the following bets: 500 , 1000 and 750 ? (I believe 500 is the best)
500 is a solid bet. It covers your opponent's win and you can double to cover his winning max bet blackjack. 750 allows you to cover your opponent's max bet double with a double of your own. Your opponent could take the low, but you could retake it by surrendering. A sim is underway to answer the question of whether giving up the low to cover a double with the option of surrender is worth the risk (asked by S. Yama on another thread). My feeling is that the cost will be too high. This situation is worse than that since you need to double yourself in order to reap the benefit. If you were giving up the low in order to cover your opponent's win, with the option to surrender, then I believe that the trade off is worth it. 1000 is an improvement over 750 in that it covers your opponent's blackjack. However, I still think that the cost is too high.
Well, it would seem that we are learning that my intuition is not to be trusted. As posted in http://www.blackjacktournaments.com/bb/showpost.php?p=47217&postcount=20, we can now see that, with surrender available, not only is it worth giving up a 1/2 swing in order to cover a double by doubling, it is also worth giving up the ability to surrender vs a push. In this case, we don't even have to give up the latter of these, so I now believe that 750 and 1000 are both superior to 500 with 1000 being the best because it also covers a winning max bet blackjack.
I ran some sims for various bets by BR1 and responses by BR2, In all cases, both players played optimal strategy: Code: [FONT="Fixedsys"] BR1 500 vs BR2 1000: BR1 Advances 67.75% BR1 750 vs BR2 248 (BR2 takes the low): BR1 Advances 63.84% BR1 750 vs BR2 496 (BR2 can surrender for the low): BR1 Advances 67.15% BR1 750 vs BR2 1000: BR1 Advances 65.71% BR1 1000 vs BR2 498 (BR2 takes the low): BR1 Advances 63.09% BR1 1000 vs BR2 996 (BR2 can surrender for the low): BR1 Advances [B]73.19%[/B] BR1 1000 vs BR2 1000: BR1 Advances 65.81%[/FONT] Once again, the best bet when betting first depends on the response of our opponent, although a BR1 bet of 500 is superior to a bet of 750 in all cases and superior to a bet of 1000 in all cases except when BR2 responds with 996. I'm still trying to figure out why a response of 996 is so much worse for BR2 than 1000.
Ok, I found the problem. There is nothing in betting 996 vs 1000 which could explain the difference in the results. It turns out that in the case of BR2 betting 996 I did not generate the optimal strategy for BR2. As a result, during the simulation, BR2 was playing basic strategy. With BR2 using the correct optimal strategy, his result is much better. BR1 only advances 63.85% of the time. With this result corrected, a BR1 bet of 500 is once again superior in all cases, which brings us full circle as that was my original gut feeling. Sorry for any confusion I may have caused regarding this teaser. My response went from "my gut says 500 is best" to "another result makes me now believe that 1000 is best" (that other turns out to be not applicable) and now back it "500 is best".
Bet thresholds ? So for this betting limits (100/1000), if BR1 have a 401 to 499 lead, he has to bet that much so with his own double to be enough to cover BR2 max bet (or total chips) double. If BR1 have a 501 to 599 lead, he has to bet only his lead minus a chip, except when he has a 500 lead and he has to bet 500. And if BR1 have a 600 lead of more, BR1 has to bet that much that he can cover BR2 double (or total chips doubled) with his own double, such as for a 600 lead BR1 has to bet 701, and for a 700 lead he has to bet 651 etc ? But what BR1 should bet for a lead of 400, 334, 333, 250 and respectively 200 ?
A bet of 2 x (lead - one chip) or 2 x lead, in some cases, has value for for all of these leads. For a lead of 400, BR1 could bet up to 798 to cover BR2's max bet win and still be able to surrender for the low. With a lead of 334, a bet of 666 can only tie BR2's max bet win but can still surrender for the low. A bet of 668 can surrender for a tie with BR2's push and beat his max bet win. I think I would prefer 668 over 666. With leads of 333 and 250, BR1 can still bet to surrender for the low and can cover BR2's max bet win with a double. For a lead of 200 BR1 can bet 400. He can then surrender for a tie with BR2's push and can double to tie BR2's max bet win.
