Last hand at Biloxi

Things have been a little slow here, so let's see if we can liven it up a little.

Ken gave me permission to use a final hand example from his just-published Blackjack Insider article (August).
For those who haven't seen it, let's review.

One advance, $10 min bet, no max, $5 increments required. Ken didn't mention it but I think it's no surrender, BJ's 3:2. Here's the situation, in betting order:

BR2 has $420, bets $420
BR1 has $425 (Ken)
BR3 has $200

As BR1, what is your bet in this situation? Of course, Ken made an excellent bet, but I thought there's a better one.

Those of you with computerized spreadsheet odds calculators, leave 'em alone. Let's make this a seat-of-the-pants discussion since those calculators aren't available when you're in a situation like this one. You're staring at that all-in bet from BR2 and the clock's ticking, but you've still got BR3 behind you. What are you going to do?

 

With 15 - 30 seconds to decide I'd bet...

I'd go with a $200 bet.

 

Match the bet of 420

 

Bet $420.00

Gives the high and low vs BR2 and high vs BR3, and 50% chance of low vs BR3

3.5 out 4 ain't bad

 

I agree with Swog

Not sure how I manage to post $200, I meant to post $210.

This will allow a DD against BR2 if needed.
It will cover push/push and loss/loss against both BR2 and BR3.
And cover push/loss against BR3.

 

I am with you, within 5 seconds I chose the match, probably not the best
but I'll go with it. BTW my second choice, maybe better was $210,
retain Double for high, still have low.

 

Anyone else?

I'll confess my decision tomorrow, see if anyone else wants to take a whack at it.

Ken brings up an interesting point that adds a variable into this problem which cannot be quantified, rendering any number-cruncher conclusions somewhat worthless. That variable is the "read" on BR3. If he/she has been a clueless bomber throughout the round, then Ken's idea that a less-than-optimal all-in bet might follow is a highly logical possibility. However, if you count on that and match BR2's bet, you could get a nasty surprise when BR3 holds back one more chip than you and forces you to win or push.

 

The 3rd way

20 would be the other possibility. By my calculation, if you assume that BR3 would be 100% sure to take the low if offered, 20 is fractionally better than 420. (But that ignores the possibility that BR3 might go all-in regardless.)

Presumably 210 is better than both if you combine it with intelligent use of the double-down option. I'd struggle to come up with a method to quantify this, though.

I think I would have bet 420 under time pressure too; it's the option that springs to mind first, and it would be my default when I ran out of time trying to think up a better one.

 

All or nothing

I still like the $210 bet for the best over all results. The $420 is more of a all or nothing bet with a greater chance of dropping to BR3 as I mention above. I'd prefer having a shot at first with the DD if needed and still keeping my best chance of dropping no lower then BR2 in case BR3 pushes.

The exception for me is if first place is just so top heavy it justifies the gamble to possibly drop to BR3.

This is just my opinion, sometimes "going for it" isn't always the best play, the best play for me is the one that allows me to come home with the most possible money.

 

My bet agreed with Swog, TX (after he corrected it ), and acemachine (second choice) - the $210.

I've got the low on everyone. Obviously I've still got the DD to take back the high although doing that would give away the low to BR3's possible small bet. If I don't DD, BR3 is toast unless he gets an all-in BJ or a full swing. I assume that BR2, the all-in first bettor, isn't that educated or he'd never make that bet - meaning there's a chance he might foolishly bust out before the action gets to me. If he does, it's all but over because BR3 can only beat me with a full swing. Even a half swing doesn't help him. If BR3 does get the all-in BJ, I can still win with the single bet. IMHO, the possibilities in my favor have increased dramatically and all I've given up is the high to BR2, which I take it back if I wish.

Having said that, Ken's $420 bet was probably the best in the situation since he thought BR3 wasn't strong enough to realize that his best chance was a small bet. As it turned out, Ken's educated guess on that was wrong.

OK, let's switch this up a little bit. For the initial scenario, there were really only two good bet choices. This time, it's the same situation except that now you're BR2, betting first. Scroll up to review chip counts. Now what do you do?

 

Makes a difference

That makes a makes a big difference, that is the same situation as a winner take all event. However I still think I'd make the $210 bet to try and lock out BR3 and still have the DD option against BR2 if needed. I just don't like giving BR3 a chance to sneak in the back door.

I'd like to see what the actual numbers are for and against for both option though.

 

Split my bankroll

As BR2 betting first I would go with the same bet $210. This would cover BR1 on a win/push or win/loss and I'd have the DD option if needed. I would also still cover BR3 on a push/win.

There is no need to hold back any chips with only one advancing since BR1 (Ken) would be betting after me and would surely match my bet ($205) giving him first high and first low and still cover the loss/push of BR3.

 

But by betting less than half your BR you can benefit if you are dealt a pair while BR1 is not. You can split and then double, taking the high since BR1 can only double.

If you bet at least $85, that is enough to cover a BR3 BJ, in the event that you do not split or double.

 

Assuming that it is still Ken sitting in the BR1 spot, I'd like to put him in a box. His most likely move is to match my bet so there's no way I can take the high. So I'd force a quandary. By betting only $15, I have removed BR3 from any consideration unless he gets a big bet BJ (which will admittedly be the end of me). The $15 bet forces BR1 into deciding whether he wants to cover BR3's possible all-in BJ and give up the low to me, OR to match my $15. If he does match, I still can DD/split to create a situation where my win over his single bet gives me the table win.

If anyone thinks this is a hideously foolish strategy, please feel free to fire away with your reasoning. :laugh:

 

I'm afraid there would be no quandary; matching is significantly better.

In a two-player game, BR1 acting second and matching BR2 has (according to Wong) .65 probability of advancing if BR2 uses Curt's Revenge, and .81 probability otherwise.

With a BR3 able to overtake with a BJ, you can just multiply those figures by .95 to get the new values: .62 and .77.

If BR1 gives up the low to BR2 he only has a .49 probability of advancing.