Last hand, no surrender, max bet 500, BJ 3-2: BR1: 700 (me) BR2: 500 Betting first, do I lead off with 195, 305, or some other amount? If I bet 195, I don't have a BR2 double covered, but if I bet 305 I give away the low.
I approach these decisions as a series of tradeoffs in probability of success. Things vary a bit depending on the rules and the skill level of your opponent, however, before the cards are dealt, the key probabilities that you need to know in order to handle most betting situations are approximately: Win a hand: 43% (includes blackjack and basic strategy splits and doubles) Lose a hand: 48% Push a hand: 9% Blackjack: 4.75% Win 2 bets (by doubling or splitting): Ranges between 6% for a basic strategy player to 32% for a very skilled opponent. So basically you cover what you can in order to increase your probability of success without giving up more than you gain. So let's go through it: If you bet 195 or less, you keep the low. BR2 must win his hand making you the favorite: 57% to 43% If you bet 305 to cover him high (he can bet the full 500, so you're not worried about a double), you're covering a 43% event but giving up 48% if he takes the low. If he is a skilled opponent, you definitely don't want to do that. Here's where knowing your opponent comes into play. If you know or suspect that he will bet the full 500 regardless of what you bet, then you can gain a huge advantage by betting 305 to cover his win. He then needs to win while you lose or push, or needs to get a blackjack while you lose your double. I think that MonkeySystem has worked out what the probability that he will bet it all needs to be in order to make this move. It gets more complex than that sometimes but as a rule of thumb, against a skilled opponent don't cover something high if it gives up something that is more likely low.
By the way, Stanford Wong's book "Casino Tournament Strategy" covers this situation as well as many others. It's a must-have for tournament players.
Thank you very much Gronbog. In this case, your post above was my line of thinking - I just needed someone else to confirm that I was indeed correct. I did download Wong's book, and he offers many examples but not quite this one specifically (I think he offers analysis for 800 vs. 500, but that is very different than 700 vs 500). It is helpful to know that I am thinking about this correctly.
He may not have used 700 vs 500 exactly, but I'm very sure that he covered not giving up the low in order to take the high while 1 on 1 and betting first.
Pretty much: "If you are BR1, you bet first, you have a slim lead over BR2, and BR3 is out of it, bet small. In other words, if you have only one competitor, you are better off trying to win the table by that competitor losing rather than by winning your own bet." Wong, Stanford. Casino Tournament Strategy (Kindle Locations 511-513). PiYee Press. Kindle Edition. The reason that I asked is because the odds change so much if you know that BR2 is going to bet the max - as you alluded to above. In the 800/500 scenario, I think you probably still bet 295. But in the 700/500 scenario, you gain a big advantage by betting 305 instead of 195.
Presumably the minimum bet in your example is fairly small (e.g., 10). If it were large enough to let you bet 305 and still have the low against the minimum BR2 could hold back, then that would become the better option.
800/500 does not qualify as a slim lead. Specifically it is greater than half a max bet, allowing you to cover both the high and the low at the same time. Wong is talking about the situation when you have to choose one or the other. Better still, in tis case, with only 500 in total, BR2 will not be able to double down in order to take the high from you. So 800/500 is hugely dominating position.
The quote above was my response to Grongbog saying that the basic situation (700/500) was covered in Wong's book. It was not in reference to the 800/500 scenario.
You are thinking about this correctly. There is a significant difference in the situation between the 800-500 score and the 700-500 score. In the case of the 800-500 score your only reasonable choice is to hold back one chip more than 500 and bet the rest. Then the simplified playing strategy is to refuse to double down unless villan has BJ, or refuse to bust any stiff hand. In the 700-500 score your choice is more difficult. If you think your opponent has at least a fair possibility of following your big bet with his own max bet, then bet at least 305. What is a fair possibility? It works out under game theory and blackjack math to be at least one-third of the time. Another way to think of it is if villan is less than twice as likely to take the low as he is to shove the max bet out there. If you don't think your opponent has a fair possibility of following your big bet with his own max bet, then bet one chip less than your lead, which makes a bet of 195.
If you think your opponent has at least a fair possibility of following your big bet with his own max bet, then bet at least 305. What is a fair possibility? It works out under game theory and blackjack math to be at least one-third of the time. Another way to think of it is if villan is less than twice as likely to take the low as he is to shove the max bet out there. If you don't think your opponent has a fair possibility of following your big bet with his own max bet, then bet one chip less than your lead, which makes a bet of 195. https://www.blackjacktournaments.com/posts/38797/
Sorry. I misunderstood slightly. Wong does cover the slim lead case in his examples as well as in the text - Example 6: 800/790, bet 5. But, whereas in some scenarios he does go into the idea that the best choice might depend on your assessment of your opponent's skill level, he doesn't do that here for some reason.
