Wong's example 41

[S. Yama]

Here is Fibonacci message on bj21.com and my reply:
Hi All!
This was an email to Stanford who suggested that we all give it
some thought:
I have devoured the bj section of Casino Tournament Strategy but I have one concern:
on pg 88 you state that if four players on last hand best is 1st High, then
1st Low, then 2nd High. On page 110 you suggest that if BR1 is first to bet that
he bet larger of br3 bankroll+ or br4 result with max win.
Using Example 41, page 111 as an example, this advice seems to concede either :
A. 1st and 2nd High to br2 and br3 (assuming they both bet big)
B. 1st High to BR3 and 1stLow, 2nd High to BR2 (assuming br2 opts for smaller
bet)
relegating BR1 to 1st Low and 3rd High in A and to 2ndH, 2nd L in B
I don't see how this can be superior to 1st hIgh although you state win
probability of .61 in the case of A and you state higher prob. in case of B.
I assume that Curts Revenge cuts into theoretical win prob but I still can't
figure out how you get to 61% for A, especially when playing hand before other players.
Thanks for any input for Greenchippers
Fib

I realize that since this was originally an email to Stanford, IO had not spelled out the details to someone without the book andy.
Final hand, $5 minimum and $500 maximum bet; Player A with $800
bets first; Player B with $700 bets second; Player C with $650
bets third; Player D with $535 bets fourth.
Should A bet max and take 1st High or should A bet $240 to cover
max win by D, thereby allowing B and C to take 1stHigh and 1st Low?
Fib


Fib,
I think you realize by now that in tournament bj there are many possibilities of “acceptable†plays and they apply to both, playing and betting strategies. Their effectiveness is often separated by only a few percents, and it is often measured by assumption that all players act in a specific way. Assuming that everybody bets maximum is the easiest to analyze, but almost never the best, and almost never happens in real life. Erroneous analysis is further heightened by the idea that most players stick to basic strategy plays.
“Casino Tournament Strategy†book (at least its blackjack section) is a great primer and it presents most of the main ideas. This is the best, alas the only book covering tournament strategy.
However, many of the numbers presented there are not so much wrong but rather misappropriated. I guess it is done in order to unify and simplify the examples but it may confuse people who read the book more thoroughly and pay attention to details.

Better way of analyzing the game is to assume the optimal play by all or at least some players. Though, it is not an easy feat. For best results, when you reach top level of expertise, you need to allocate percentages for chances of each player making particular bet (and plays) and figure out your optimal play.

Back to “Casino Tournament Strategy†example 41. The 61% chance of BR1 advancing with the bet of 240 had to be achieved by deducting chances of:
A and B winning regardless of BR1’s result, and
A and C but not B, and B and C but not A winning while BR1 pushes or loses, and
A or B but not both winning and C receiving blackjack while BR1 wins.
I think the numbers didn’t reflect an often-beneficial Player C doubling down for rest of his money and possible (but not basic strategy) double downs by Players A and B. Also, it doesn’t include, sometimes necessary, plays where Players A, B and C draw to a total that is bigger than BR1 hand.
The difference between 61% and 57% is caused by chance of receiving a blackjack with the bet of 240 (it would bring BR1 to 1160- which is more than what Player A would have if he won max bet).
Last sentence in the description of this example, “355, to cover a max-bet win by BR3, is inferior to 240 no matter what your opponents bet.†is also false. If everybody bets big 355 bet is superior to the bet of 240.


For discussion of tournament bj you may check message boards (forums) at: BlackjackTournaments.com/bb/
It deals with tournament issues only.

Hope it helps,
S. Yama

 

[rondog]

just a little confused

i have played a lot of tournaments but still often bet wrong. i have a question about the issue above.what about a bet of 405? that would give first high with max bet of any player allowing for a first or second low if they do bet max, but also allowing for one other player to bj or win a win double down leaving playera in second. that would also allow player a to double down if say two players have have tens or elevens against a dealer 6 or a similar situation.

 

[S. Yama]

Train of thought and more numbers.

Rondog and others,
Firstly, I think this case may be too complicated to serve as a good example for thorough analysis. I can’t write about it without being hard to understand, obvious, and fragmentary… all at the same time.

Note that the player with the biggest bankroll has the worst betting position, and the second biggest bankroll has the second worst betting position, and so on. This compresses chances of advancing for all players and makes the case more difficult to tumble. But if you are willing to take a piece of paper and write down different scenarios and scrutinize them we can give it a try.

Many players mistakenly pick one particular bet, or play, out of tens possible, and compare it to just a few other possible choices. It may work sometimes but it is not a reliable method.

Often times it is impossible to assimilate complete field of action so it may be helpful to:
1. Start by identifying a general situation.
2. Check if you can determine “directional†type of action required of you. It may be a decision whether to bet “a high†or “a lowâ€, or realizing than you can not afford to lose your bet, or that you need a full swing to your main opponent, and so on.
3. Compare and find bet ranges that provide most benefits (best chances). This is usually the most calculation intense and detailed part.
4. Consider your opponents’ bet/play patterns and their anticipated reactions to your specific bets/plays, and weigh it against your best chances derived in p.3. Sometimes certainty of other players’ act is strong enough and so consequential that it should be implemented right after identifying the general situation.

Let’s go to Wong’s example #41.
Last hand, four players, BR1 (P1) 800, BR2 (P2) 700, BR3 (P3) 650, and BR4 (P4) 535.
Two players advance, bets are min 5, max 500, no surrender.

1. Generally, with four contestants who have some tournament experience and two players advancing there will be a polarization of goals. That means that two players will take a low and two players will take a high.
Note that because of relatively big bet limits and not so big differences in players’ bankrolls, it is infeasible to have both, the high and the low. (The lowest-money man can go to 1,035 by winning single max bet; to cover it BR1 must bet at least 240, losing of which drops him to 560. 560 is less than starting bankrolls of the two other players; Effectively BR1 losing 240 also loses chance of being ahead of the other two players if they push.)
From the perspective of P1, whether to bet low or high depends on more detailed conditional analysis of probable P2’s bet, which is conditional on probable P3’s, and than P4’s, bet. However, approximation of chances to advance should not be that difficult to calculate.

2. Let’s start with a high. If P1 bets big then two other players will take a low. So, chances for P1 to advance are limited to when he wins his hand and to most of pushes (except when the other high bettor wins and one of the low bettors bets big enough and wins). This should be in the neighborhood of 51%-52%.
If P1 chooses to bet low, he always advances except when both high bettors win their hands, and some cases when one or the other (but not both) high bettor wins and the other low bettor bets big enough and wins. Total chances in % would depend on other players’ skills and should be in the range of high fifties to high sixties. For good players they should be close to 65%.
Betting low is decisively better option for P1.

3. P1 should bet low. What low is the best low?
There are some obvious ranges: Bet of less than 100 – even if the bet is lost, P1 will have more than the player with the next biggest bankroll pushing his hand. Bet of less than 150- to keep more chips than the player with the second biggest bankroll pushing; and so on. There are also ranges of bets that help improve P1 chances even more. They are based on his anticipation of other players’ bets. For example, we can define a bet of less than 100 by noticing that if P2 chooses to bet big, then P3 is very likely to bet just short of his lead over P4, which is 110. With the right conditions (only one of high bettors winning) P3 needs to overcome P1. If P3 doubles his bet of 110 his bankroll grows up to 870. It is easier for P3 to win a doubled bet than to full swing P1, therefore P1 needs to bet between 75 and 95 to have a chance to have more money than P3. Also, P1 needs to switch his playing strategy from the basic strategy to “not to get swinged†strategy. Since some players often make a mistake of betting not less but exactly the difference between the bankrolls, e.g. P3 may bet 115, and to protect himself from it P1 needs to bet 85 to 95.

4. In the above example it is unlikely that players would make bets other than decisive two lows and two highs. However, if you play against novices, or if you know that one or more players have a tendency to bet in a specific way, for example he always bets a max, or always bets half of his bankroll, you need to decide if deviation from previously calculated play is more beneficial. If everybody makes big bets, so that you have both the low and the high, but the high can be taken away from you by your opponents winning a doubled bet or by receiving a bj, you may calculate that your chances to advance are about, let’s say, 80%. If you take a low and everybody bets high your chances may be about 55%. Now, you need to assign how probable it is that all three players will bet high. You may think that about a third of the time they all will bet high and two thirds they will take two lows and two highs. If you bet high, one-third times 80%, plus two-thirds times 52% equal just over 60%. If you bet low, one third times 65%, plus two third times 55% equals about 58%.
Conclusion: you need to be at least 30% sure that all players will bet big to make a big bet yourself.

S. Yama

 

[rondog]

thanks

thanks for your reply s.yama i think i get it.