A small teaser

This might be a bit too obvious to be called a teaser, but I have to admit I misplayed this situation a number of times before I saw the error of my ways -

Last hand; two players.
Min Bet: 100, Max Bet: 500, No Surrender.

BR1: 1401
BR2: 1200

BR1 to bet first. What should the bet be?

 

300

 

400

 

Are you sure? Did you notice "No Surrender"?

 

I think 200 is the best bet

 

$300 and why!

My bet would be $300.

Reason: assuming BR2 bets $500 and we both win, I cover them by $1, forcing them to get an extra bet down by DD or Spliting to go for the win. And should we both lose I still cover them.

Now the $200 bet is good in case of a push swing. Where BR1 loses, while BR2 pushes. BR1 still covers by $1.

But I'll take my chances on the same results vs. any type of swing.

 

300 it is

But I fell into the trap of betting 200 on a number of occasions before I suddenly had a moment of 'what the heck am I doing?' clarity.

I had been blindly applying Wong's 'bet your lead minus a chip' advice, without considering the impact of the unusually large min bet of 100. If it were smaller, then 200 would be the right bet, forcing BR2 to bet big and win the hand. Bet any more, and BR2 could take the low.

However, as Rick says, a bet of 300 covers both the high and the low in this case, whatever BR2 bets. A push being much so much less likely than a win or a loss, it's better to cover the both-win and both-lose cases, and forget about the push.

If the lead were 251, rather than 201, then the best bet would actually fall to 250. That covers the push too, without giving up the high.

 

Exactly my conclusion, too. Didn't want to give it away immediately, since arlalik had come up with it right away.

Without the "No Surrender" rule, bobh4545 had what I'd believe is the bet with the best chance.

Great teaser, Colin, and I hope some of the newbies tackled it!

 

300 vs 200

300 is better than 200 just because the min bet is 100. That means you advance with lose/lose also with br2's min bet.

 

That's a subtle one. I'm certain I would have bet 65 too.

Suppose surrender had been allowed? Regardless of the min bet, is 135 now the best choice? Twice your lead is just enough to cover the high, so it's not possible to incorporate the 'minus a chip' part of the usual formula. A surrender risks a tie with a BR2 push, but again the tradeoff seems favourable.

 

Just a teaser...

I understand this is just a teaser London, however with a $100 minimum and $500 maximum bets. I was wondering how BR1 got the single $1 ($1,401)...LOL

Just messing with you, I know it was just numbers for the example.

 

No Tex

The $1 is real. Both GameAccount and Blackjack21 have min bets of 100, but what I tend to call a 'betting increment' (for want of an official term) of $1.

Blackjack21 has a max bet of 1000, compared to GameAccount's 500. The equivalent lead would be 451, where a bet of 550 covers high and low. Except surrender is allowed, which changes everything.

 

A follow-up

Same situation as the first example, but this time the lead is a bit bigger -

BR1: 1501
BR2: 1200

Is 300 the right bet?

In the first example, I knew I was wrong to have bet 200. This time I only suspect 300 may be wrong, so I hope to find out for sure.

I have an alternative in mind. Actually a small range of bets at first seemed to be equivalent, but I came up with a reason to prefer the low end of the range.

 

Any bet between 350 to 400 gives you the high and low plus if BR2 makes a max bet and gets a good DD opportunity or a BJ, you can still win with a DD if need be.

I'm curious, London, why you think going with the low end of the range may be preferable - assuming, of course, that my range is what you had in mind.


PS: Maybe a bet of 375 would confuse BR2 into making a bad bet given the time limit to make a bet. Just a thought.

 

Here is the situation once again:
Last hand; two players.
Min Bet: 100, Max Bet: 500, No Surrender, BR1 bets first, what should their bet be?

BR1 - $1,501
BR2 - $1,200

The bet depends on what you are willing to give up!
A $300 bet by BR1 covers a straight up max bet and win by BR2, but allows for a BJ and or DD, split to possible beat you.

However BR1 is covered on a BR1 loss/BR2 push swing.

With a $350 bet, BR1 can have a DD option should they need it. However they guve up the low in case of a BR1 loss/ BR2 push swing.

With a $450 bet by BR1, they can cover BR2's BJ, but gives up the low. I don't like this bet at all.

I actually perfer taking the low most times, but here I like the $350 bet and here is why.

1. As BR1 it allows me the chance to DD and or split if needed.
2. No Surrender.
3. Less chance of being swung, then both BR1 and BR2 having the same results.

Just my opinion.

 

It's not just that you have the opportunity to rescue yourself against a likely winning BR2 DD or a BJ. If BR2 bets the max, then your doubled 350-400 bet will still leave you with the low if you should lose it. So if you want to take a card and are reasonably unlikely to want to take a second one, then you might as well double.

Even if you bust, the only down-side is that BR2 now has the fexibility to just play their hand according to BS [*], rather than think about a forced double versus playing for a swing.

If you don't bust, BR2's only option is to play for a swing.

[* Not quite BS, since a push is as good as a win.]

Suppose BR2 bets less than the max? In particular, 400 seems like a plausible bet. I neglected to mention that there is no DD-for-less in this game, making 400 the only way BR2 could go all-in with a split and DD, but even without this detail there is still the chance to re-split which would not be available with a bet of 500.

If you bet 350 then that's enough to cover a BR2 DD of any size, but it also means that if BR2 bets at least 400 you can safely DD and keep the low -

BR1: 1501 - 2*350 = 801
BR2: 1200 - 400 = 800

That being said, maybe BR2's best response would be to bet less. A BR2 bet in the range 326-398 will be enough to DD past a BR1 single-bet win of 350, while at the same time making BR1 think twice about doubling (or possibly regret it if a DD results in a poor hand). All BR2 would be giving up is the possibility to benefit from a BJ.

 

Yeah, and I would guess that you gain more from covering the DD than you lose from risking the lose-push, making the tradeoff worthwhile. It's just that this seems like a very tricky thing to evaluate, and I'm really just going by gut feeling.

Plus, I imagine the optimum strategy for BR1's choice between DD/Hit/Stand might be quite involved. I would guess it often comes down to a choice between DD and Stand (assuming BR2 has bet big enough to allow a DD that keeps the low). As I mentioned above, often I would expect that if you are going to hit, then you may as well double to get the maximum benefit.