Last hand at Biloxi

Dear Yama (ha?!!) :laugh:

Thank you for your appearance.

I am afraid I don't agree. In my view optimal play is one that you consider the MOST PROBABLE OUTCOMES, not all possibilities.

To me, one of the betting principle is, as I mentioned previously, putting a SINGLE bet into the first priority. Always consider a SINGLE bet win/loss ahead of anything else (e.g. double, split, push, blackjack, etc.)

If you do not agree with this principle of mine, you are welcome to debate.

Frankly speaking I have no idea how you worked out that 48.5% figure (you could be right. . I can only use my logic and common sense to draw a conclusion. Like I said above, I do not think putting all possibilities together is the right path, rather, I am interested in the MOST PROBABLE and STRAIGHTFORWARD outcomes.

Betting anything below $20 is the optimal bet. Generally $5, $10, $15, $20 all do the same thing - they all guarantee your advance if BR2 loses or BR2 and you push, while locking out BR3 even if he wins (excluding an all-in blackjack win by BR3). You only need to make sure you don't double or split your bet when betting anything above $10 to avoid a single win swing by BR3.

 

Yama (ha

If you read my posts carefully, you will see I have been talking about the MOST PROBABLE or HIGH PERCENTAGE outcomes.

Yes you gave me all things to consider, but like I said, in my view only MOST LIKELY occurrences matter.

As for the bet of $210, personally I think it is an ESSENTIALLY wrong bet so will not try to discover any imbeded merits of it.

 

Oh just one thing: I think it might be good to mention that in my local casino's BJ tournament here in Australia, players are only allowed to double on 9, 10 and 11. Of course we have fewer chances for doubling, however I still hold on to my own principle of betting: always consider a SINGLE bet win/loss ahead of anything else, which is most probable.

 

This discussion is getting nowhere because there is a basic lack of agreement of the definition of "optimal". The dictionary defines "optimum" ("optimal" is the plural of "optimum") as "best or most favorable". This is the principal used by mathematicians to calculate probabilities. Those probabilities are normally a combination of all possible occurrences which result in a course of action that will give, over time, the "best" probability of winning. garygo is defining "optimal" differently:

garygo's definition of "optimal" differs from the dictionary and how the word is used in every day use. Of course, if one defines any word in one's own way and to suite one's own needs then that person will be led astray although that person will feel right in his/her own mind.

The bottom line is that an optimal bet is indeed a combination of all possible outcomes. Just using the "most probable outcomes" ignores the outcomes that occur infrequently but enough times to change the odds possibly significantly. For example, a casino would love one to play live Blackjack if one would always assume the dealer has a 10 in the hole - the "most probable outcome". That would give the casino a huge advantage - maybe 5%, 10%, or even 15% because a player would be hitting a hard 17 against the dealer up card of 8 because, of course, the dealer has 18.

In the scenario at hand, a $20 bet is a "good" bet if one's mind turns to mush or time prevents a more careful analysis. However, $20 is not the "optimal" or "best" bet because some other bet amounts result in a greater probability of winning. Live Blackjack and Tournament Blackjack are all about the math - OK, and a very little reading of opponents in Tournament play. It's really that simple!

 

Thanks for your contribution toolman1.

I am afraid optimal is an adjective, not a noun. Optima is the plural of optimum.

I don't see any discrepancy between my understanding of optimal and the dictionary's definition. All I've been talking about is "highest percentage play / most probable outcomes", which is in essence identical to "best or most favorable" and "best probability of winning" that you mentioned above. What is the difference?

I am sorry but this is not true. When there is a distinctly high probability that occurs to you, at the blackjack tournament table you don't have to go through all other possibilities like a computer. And guess what? Even if you do go through the combination of all possible outcomes, you will probably arrive at the same conclusion: the most probable outcomes. Most probable outcome is no doubt the golden rule.

Let me give you a simple example: say you are BR1 with $650 and BR2 has $600. BR2 bets ahead of you and places $300. What should you bet?

Obviously it is wise to simply match his bet by betting $345 to have both the high and the low. But BR2 can double or split to reach $1200, or he can get a blackjack and reach $1050. Should you bet $405-$555 to cover those possibilities? Of course not. If you do, you will sacrifice the pure low!

This is a textbook example to show what MOST PROBABLE OUTCOMES VS ALL POSSIBILITIES is. I am afraid it renders invalid this claim of yours: "Just using the "most probable outcomes" ignores the outcomes that occur infrequently but enough times to change the odds possibly significantly." In this case, BR2's blackjack, double and split win are all "outcomes that occur infrequently", however, our wise choice is simply ignore them and go for the "most probable outcome", that is the SINGLE bet win/loss (remember my priority betting principle?)

This type of examples are everywhere - even in Ken's ebook "How to win more blackjack tournaments", which I am going to comment on in the coming week.

It seems that your mind turns to mush here by suggesting other bet amounts have a greater winning probability.

Let's use example for this debate. In this situation if you place $420, your only hope of advancing is you win! And as I said, this bet is not even a pure high, as BR2 can get a blackjack to lock you out. And you are exposed to BR3's pure low.

With a bet of $20, you secure a pure low against BR2, and a lock against BR3.

Which bet amount has a greater probability of winning?

 

A further pondering:

A bet of $210 is an interesting bet, as it gives you the flexibility to change your play strategy even after cards are dealt. The main advantage of this bet is: you keep the low against two opponents, while retaining the ability to take the high back if needed.

Now let's look at the major disadvantages of this bet:

1) If you are unsuccessful in doubling/splitting, you are out. Remember, when you double down you receive one card only, and if you have a busting hand you have very slim chance to survive! Also, if you split, you will have to win both hands.

2) If you lose your hand and BR3 wins, you are out.

3) Once you double/split, you are giving up the low to BR3, which is against your initial intention.

After all, how likely will you have to double/split to take the high back? And how likely will you succeed in so doing?

Simply put, if you have to double/split to take the high back, $210 is inferior to a $420 bet. If you keep the low, $210 is inferior to a $20 bet which ensures a lock to BR3 (no swing by him). I don't think it is possible to cover both worlds - betting in the middle in this case is just meaningless.

The most probable situations are SINGLE bet win/loss. Thinking too much only makes things complicated.

 

I am a newbie to the blackjack world (only 8 months' experience), but I believe any optimal play should combine mathematical calculation and logical thinking/reasoning. If you rely too heavily on those techinical stuff, you will be complicating situations and lock out simplicity.

I found blackjack tournament is amazing to discuss as it involves so much brainstorming! Let alone the possible big prize to win if you attend one.

Now I would like to know:

1) What do you guys think about my choice as follows:

My comment:

Ok, now for this situation, if we use the same logic and thinking process, it is not hard to work out the best bet for BR2: $15. (For detailed explanation please refer to my proceeding post on this)

2) In my local casino's BJ tournaments, players are only allowed to double on 9, 10, 11 (I've just realized it is allowed to double on any card in the US). So in the Australian situation, what will be your consideration in terms of optimal play? I am sure we will have to adjust our play and betting strategies, right?