So. With all strategy available. Betting first with lead on final hand is still a dilemma. Gauge your opponents and do a standard lead minus a chip, or employ Money bet for multiple options still does not account for two players behind you to make the best bet of doubling hard count, or going all in. You can win, but if they win behind you, with hard doubles or all ins you lose. Even if you'd win with max bet BJ. So it goes.
My mind has been somersaults over this question for days. I get the lead - a chip strategy when the lead is greater than half the Max bet but how do you bet when your lead is less than half a max bet? Specifically with only once person in contention. Wong says to bet the minimum and hope your opponent loses but I hate leaving myself open and powerless with such a small bet. HELP!
With a savvy opponent, the small bet is best. However, in many cases you can use this idea... 1) "Well, these things always come down to the last hand. Let's see who gets the better cards..." 2) Push a max bet in the circle. If you think your opponent will match your max bet in even a relatively small percentage of times you try this, you're better off with the big bet. Remember, even if your opponent does the smart thing and keeps back more unbet chips, you still win with W/W, W/L, P/P, and P/L outcomes. If he foolishly matches your max bet, he must swing you to win. I'm out of practice and also don't have sources easily at hand. Anyone want to put numbers on this again?
Thanks for the quick response and love the website. Bought your ebook today. Would it be possible to have the tournament filtered by number of decks used? Just a thought. I'm not sure I fully understand the rationale of betting the minimum with a small lead. Let's say for example player A has 2000 and B has 1900. $100 min. Player A should bet $100? If you were player B your only choice is betting $200+ to beat player A of you can get a swing right?
With only one other player, the rationale for betting low (keeping the low) is your opponent must win the hand to beat you. He will win about 44% of the time and thus you will advance about 56% of the time. If you bet high and allow your opponent to take the low on you, then you must win or at least push (assuming your opponent pushes or loses) to advance. That is approximately 48-49% of the time. On the bubble (in a crowd), normally your best bet is going to be the max, unless you have people like the "out of practice" Ken behind you and then you keep the low. I believe the best overall source of information on tournament strategy is Stanford Wong's "Casino Tournament Strategy". You might find it in a half-price book store.
Fuzzy Math My rule of thumb in this situation is, you think your opponent has a "fair" chance or better of matching your max lead off bet with his own, then bet the max. By "fair" I mean 1/3 or better. 1/3 means your opponent is twice as likely to take the low as to follow with the max bet. But since your advantage is so huge if he does that, and since you don't lose all that much if he takes the low versus if you bet the minimum, it is a profitable play in the long run. This actually works out mathematically. But since you can't put hard fractions on human behavior I use "fair." When assigning fractions to human behavior so you can give it mathematical treatment like this, think of a 1/3 chance as "fair," a 2/3 chance as "strong," and 1/2 if it's a coin flip or if you have no idea.
For the actual situation posted by Chicago1972, there is the possibility that Player A will lose while Player B pushes, resulting in a tie.The lose/push swing happens about 5% of the time, which decreases Player A's chances of winning by 5% x his probability of losing the tie breaker. Even in the worst case scenario where he has a 100% chance of losing the tie breaker, taking the low still yields and advantage of 51% vs 49% for taking the high.
You didn't say what the max is here, however, Player B should probably just bet the max, whatever it is, in order to cover as many player A outcomes as possible. He would want to at least cover Player A's blackjack and double/split with his single bet, if possible. One could calculate the exact amount needed to do so, but, if it's the final hand, then simply betting max covers as many outcomes as possible without any mental effort which, in turn reduces the chance of making an error.
I think that with what we know about the probabilitiess of winning, pushing and swinging hands, we can put some actual numbers on Monkeysystem's rule of thumb. Just to be clear, this is the situation where you lead your opponent by less than 1/2 a max bet and are acting first. If we bet small, as discussed earlier in this thread, we advance if our opponent loses or pushes his hand and our probability of advancing is approximately: L = 0.56 If we bet big, and our opponent takes the low, we advance if we win our hand or if we push while our opponent loses or pushes his hand. The probability of winning our hand is about 0.44, the probability of pushing while our opponent loses is about 0.051 and the probability of pushing while our opponent pushes is about .012. So our overall probability of advancing would be approximately: H = 0.44 + 0.05 + 0.01 = 0.50 If we bet big and our opponent foolishly matches our bet, we advance as long as there is no 1/2 swing. Let's call this probability C for now. If we then let B = the probability that our opponent will match our big betthen our actual probability of advancing with a big bet is: BC + (1 - B)H ==>BC + (1 - B)*0.50 In order to prefer making the big bet, we therefore need BC + (1 - B)*0.50 > L ==>BC + (1 - B) * 0.50 > 0.56 ==>BC + 0.50 - 0.50*B > 0.56 ==>B*(C - 0.50) + 0.50 > 0.56 ==>B*(C - 0.50) > 0.057 ==>B > 0.057 / (C - 0.50) Now, C depends on the skill level of our opponent. The two extremes are that he is a basic strategy opponent or he plays optimally. For a basic stratey opponent without enough chips to double/split, C = 0.81 (How To Win Even More Blackjack Tournaments, Volume II, chapter 16, and verified using my simulator)so we would need B > 0.07 / (0.81 - 0.50) ==> B > 0.23 before we would prefer betting big over taking the low. For a basic strategy opponent with enough chips to double/split to 4 hands, C = 0.78 (obtained using my simulator)so we would need B > 0.07 / (0.78 - 0.50) ==> B > 0.25 before we would prefer betting big over taking the low. For an optimal strategy opponent without enough chips to double/split, C = 0.76 (obtained using my simulator)so we would needB > 0.07 / (0.76 - 0.50) ==> B > 0.27 before we would prefer betting big over taking the low. For an optimal strategy opponent with enough chips to double/split to 4 hands, C = 0.63 (obtained using my simulator)so we would need B > 0.07 / (0.63 - 0.50) ==> B > 0.54 before we would prefer betting big over taking the low. So, depending on the skill level of our opponent, we're looking for something between a 23% and 54% chance that he will match our big bet before we would favour it over taking the low. Now, the 54% scenario is unlikely because we not not expect someone who matched our big bet to know the optimal strategy for overcoming that bet. In reality, such a player would double or split more often than called for by basic strategy, but would do so far from optimally. Also, when he does not have enough chips to double or split, the range is a more manageable 23%-27%. For a long time, I have resisted ever giving up the low on the final hand. However, this is one aspect of my game that really needs to improve and, from what I've learned in this thread, I will definitely be doing it a lot more in some of the events that I play.
One more bit of information. In the cases where I said that our opponent has enough chips to double or split up to 4 hands, the numbers are almost the same even if they have only enough to get 2 bets on the table. That is, most of their leverage comes from being able to double or to split once.
Thanks Larry. If folks appreciate the things that I post, then I will continue to do so. Also thanks to S. Yama for contacting me privately in order to point out my incorrect calculation of the probability of advancing when we take the high and our opponent takes the low. He pointed out that the push/lose and push/push outcomes are correlated, so the correct probability of advancing is approximately 0.44 + 0.05 + 0.01 = 0.50. I have corrected my original post and all of the results which follow. I have kept the results to two significant digits for the sake of usefulness. I don't think that any of us could read an opponent so accurately so as to require fractions of a percenatge point.
Human (Or Simian) Behavior You're exactly right, Gronbog, which is why I round it to 1/3. 1/3 is a convenient fraction because it means that one of the two possibilities is twice as likely as the other. Estimating human behavior is not an exact science so we need to use terminology like "fair chance" or "strong chance" rather than exact fractions or percentages. Once we assign a possbility a "fair chance" then we can proceed to assign convenient fractions for the purpose of mathematical analysis. 1/3 seems like a good "fair chance" and it fits nicely with the mathematics of this situation. The kind of opponent who is likely to make the optimal use of doubling down, Strong Variation of Curt's Revenge, etc. probably doesn't have even a "fair" chance of following your max bet lead with his own max bet. Against such an opponent you would lead off with a small bet that holds back one more chip than that guy's bankroll. I've been in a couple situations like this. Knowing how big my advantage could be if the opponent matches my max bet, and having seen how often they do that, makes throwing my max bet out in the circle very tempting indeed.
I got this from another forum... Ignoring player 3, the thing is, why is betting the minimum preferred? Isn't betting the max and hoping to win the same thing as betting the min and hoping dealer wins? I think it all comes down to who gets the best cards, right? Not sure how we can say that betting min. is THE best strategic manuever if 2 players were tied going in and you are on the button.
Don't Ignore Player 3 What forum did you get this from? You wouldn't ignore Player 3 at all in this scenario. Player 3 has enough left to get all his money in with a double down. You need to cover that, by betting at least 225. As long as you're betting 225 you might as well bet 500. You can't cover Player 3's double down without risking a full swing against Player 3. You can't lock out Player 3. Not only that but the existence of a down-but-not-quite-out BR3 should alert you to possibility of giving your opponent (in this case Player 2) the opportunity to make a mistake. Many conservative players will hesitate before opening a door for BR3. It looks like Player 2 did just that after you led off big. Your bet of 500 forced Player 2 to bet at least 275 to be able to take the low with the chance to double for the high. He would have to risk the full swing to do that. It might give him pause. Alot of players react by betting too small against a maximum lead off bet when BR3 can get the swing. Player 2 made a weak bet. He wasted any blackjack or strong double down opportunity he might have gotten. He failed to cover Player 3's double down. He robbed himself of a chance to double on anything in case you got a strong hand. His bet of 25 and rooting for the dealer is absolutely no different than if he had bet 175. If Player 2 bets 475 he still has first low. He covers Player 3's double down. He can cover your single bet or blackjack with his double down. His blackjack forces you to double down. The only tradeoff is he risks a full swing by Player 3. To make a long story short, you made a good bet, and Player 2 made a mistake that could've helped you. It's more than just a game of luck. But those cards were a train wreck.
I said to ignore player 3 because I am only interested in knowing what I specifically asked... that is, involving only 2 players (thus myself and player 2) and how is betting the minimum any diff. then betting the max and hoping to beat the dealer? See my previous post, thanks.
