BR3 of 3, Last To Act, 2 Advance

Well, dang! I never said I made the very best bet. However, I was playing the players as well as the odds. Strong opponents would have caused me to make that 300 bet. BR2's obvious confusion led me to believe that the 400 bet would make him think that he had to double/split anything and I'd have the option of acting after him, which is exactly how it worked out. Lucky me, eh?

 

Tables say Bet 300

Using three player outcome tables and BJ paying 2-1 the following results are obtained :

When BR2 bets 200:

Then any bet of 300 or less by BR3 yields a chance greater than 50% for BR3 to advance. A BR3 bet of 50-80 yields a 56.28% chance for BR3.

Increased BR3 bets yield slightly higher chances and a BR3 bet of 300 yields a 59.82% for BR3.

A BR3 bet of 310 yields a 44.29% for BR3.

A BR3 bet of 320-370 yields only 28.76% for BR3.

A BR3 bet 0f 400-500 yields 48.89% for BR3.


A BR2 bet of 170 does not change things much:

A BR3 bet of 50-80 yields a 54.43% for BR3.

Increased bets by BR3 slowly increase his chances and a BR3 bet of 270-300 yield a 57.97% for BR3.

A BR3 bet 310 yields a 42.44% for BR3

A BR3 bet of 320-340 yield only a 26.92% for BR3 to advance.

A BR3 bet 400-500 yield a 47.04% for BR3.


..................................BlueLight

 

Well no. But Monkey thought that you may have done, for the reasons he explained.

But BR2 did have to double/split (almost?) anything. It's the correct play, a free double, giving the opportunity to correlate with your bet and still have the low on BR1.

(There are probably some scenarios in which standing and hoping you or BR1 push is better than doubling. I'm getting a little confused thinking about this, though.)

And acting after BR2 is just as advantageous with a bet of 300 as it is with 400.


As I said in an earlier post, the only way I can see to factor expectations of opponents' bad play into your own bet is if BR1 was a pathological doubler. I can't see anything BR2 can do (or fail to do) that makes a bet of 400 preferable.

 

Thanks for providing those numbers, BlueLight.

I take it the above figure does not factor in the additional Curt's Revenge-like possibilities. Presumably that will add another 5% or so?

Thanks for the kind words.

Truth is I struggled in vain to come up with a way of arriving at BlueLight-style, definitive figures, before it finally occurred to me that I could take an easier option and just look at the upper/lower limits of what each bet must be worth.

 

Figures for bet of 300

My figures for a BR3 bet of 300 are for all 3 players playing the basic strategy for hitting and standing only. No doubling or splitting is considered.

No hitting beyond hard 17 for BR3 is considered even when BR1 and BR2 have good hands. For example if BR1 gets a BJ and BR2 gets a hard 18 then BR3 must hit to 19. This extra hitting is not considered in the tables. How much extra gain BR3 would get is impractical to figure and can be only a guess. However after the cards are delt and BR1 and BR2 have acted on their hands then it can be figured.


.......................BlueLight

 

That's what I thought. Just wanted to be absolutely clear.

My guess of 5% came from the two-player case in Wong's Example 19. In that case BR2's basic probability would be about 50%, but is boosted to 55%.

I was thinking purely in terms of doubling as the source of this gain. You make a good point, though: when Curt's Revenge is not appropriate (because of the high chance of the opponent not winning), free hits are the next thing to consider and will also contribute to the gain.

With two opponents, I suppose there may be less doubling and more free-hitting for BR3, compared to BR2 in Example 19.

 

300 vs. 400

I guess, my advice would be to try to see and add up total chances for “each side” of a particular bet/play. There may be different ways of grouping it together. But it is important to look at all results of one participant multiplied by all other necessary results.

For example, we could look for:
a) All possible results of my hand (win double/bj/push/lose the bet) and see what needs to happen to my opponents, in order for me to advance (or not advance – but we try to score only one aspect).
b) Take all possible results of the first opponent and what needs to happen to us, and then all possible results for the second opponent IF the plays against the first opponent didn’t meet that same aspect (my advancement) we trying to calculate.

Back to our case, the analysis for comparing 300 and 400 bets could go like this:

If I bet 400
If I lose -- I advance only if BR1 doubles (very unlikely) his 500 bet and loses, or if the dealer has an Ace up, BR1 doesn’t surrender, I do, and the dealer has blackjack, or BR1 still loses. The chance – less than 1%
If I push – I advance when either one of them loses. The chance - almost 7%.
If I win – I advance in most cases, except when BR2 wins double bet, and at the same time BR1 wins and I don’t win double. Since BR2 will have incentives to double more often than basic strategy calls for (it is for BR2 almost a free double) the chance, depending on BR2 plays, is about 35%.
That’s all, it adds up to less than chance of a simple win. Total chances for bet of 400 is about 43%.

If I bet 300 (keep low to BR1) I advance when:
BR1 loses – that’s about 48%, right there. Minus (about 2% gain) if he surrenders otherwise losing hand and I lose, and when I feel pressure of doubling after BR2’s good looking double and lose. My chance about 45%.
BR1 pushes and I win, or I push but BR2 loses – that adds up to another 3%.
BR1 wins – my only chance is to gain to BR2 (my double win/ to his single win or worse, win/push, and push/lose). This again will vary based on players’ skills but could be about 25% to 28%.
Total chances of advancing from the round with 300 bet are about 63% to 65%.

S. Yama