Reachy/Sabrejack Showdown Analysis

Yes, behind that very serious title is bit of only semi-serious play analysis. Since it was not only Reachy and I, but also onlookers TXTP and Jackaroo (providing expert commentary and mildly distracting golf banter), I thought it might be entertaining to hear post-commentary and of course ask:
"What Would You Do?"

The Set Up--
Elimination BJ
2nd Last Hand
Sabrejack (me): BR3 at about 31K
Reachy: BR2 at about 39K
3rd Player: BR1 at about 41K
No one has a secret bet left due to earlier warfare
Only two advance

Betting first, 3rd Player bets 500
Reachy, failing to "reach" his bet button, is auto bet 500 as well
I bet 11K, hoping to swing

Dealer Ace (all waive insurance--no BJ), 3rd player and Reachy get to comfortable hands (18, 20 or so). I've been dealt everyone's favorite: H16.

I analyze: Two hands to go, I can only swing this hand or next, then it's all over. If I surrender (the correct play), I automatically give one of those two swing chances away. Of course, having 25.5K instead of 20K would be useful on the final hand, but not useful enough to guarantee a win above my competitors with their superior bankrolls and our lack of secret bets.

So, I hit. And I bust. Reachy pushes and 3rd wins, but their bets were so small they mean nothing big picture. But now I have one chance left to swing and have not depleted my BR beyond the point where I can be a threat.

The last hand isn't that interesting (at least for me!) because I bet my remaining 20K of course, Reachy sized his bet to win if I won or pushed, and the third guy was untouchable anyway, barring a BJ, which he did not bet enough to be clear of. Only a BJ could have saved me and that did not occur.

Thoughts? Maybe I'm wrong!

Here's hoping Reachy is still in there for Team BJT.com as I write this! Onward to the next battle...

Good cards (and BJs at the right time) to you all--Sabresport/Sabrejack


(Disclaimer: I'm sure some of these details are slightly off, but this is the gist of what went down)

 

On the button

Your memory serves you well Sabre as I think you are about right with BRs/Cards/action. I was only slightly upset that I didn't get my bet out as I was going to take the low road anyway. Would have been nice to have a bit more on top and to take the high on BR1 but it all came out in the wash

Unfortunately I didn't make it past the next round and never really got any cards. In fact in all 3 rounds I played the dealer was tough. Excuses, excuses...

I did enjoy the game though. It could have gone any way right until that last hand.

Cheers

Reachy

 

Surrender

sabresport:

Before I comment on your play, let's clarify the term "swing". A "swing" occurs when one person wins and the other loses - thus a "swing". In your second from last hand, all you needed was a win to be in the lead irregardless of what happens to BR1 or BR2 (unless either doubles or triples, etc) - no need for a swing.

As for the betting, I would have bet a little more - maybe $12,000. Since BR1 already bet $500, a $12,000 win would assure you of at least the #2 spot even if BR1 doubles or triples.

As for playing, as you know, you are in a bad position, so surrendering was your best play in my opinion. Your 16 against a dealer Ace is really no match (I would have surrendered a 17 also). Your chances of winning or pushing are pretty small and a losing $11,000 makes your chances of winning the table on the next hand small. By surrendering, the last hand becomes more doable for you since you have enough money to challenge BR1 and BR2. You now have a chance for a "swing" if BR1 or BR2 bets are big or a simple win if BR1 or BR2 takes the low.

 

Welll....I don no...but.......

If you're gonna use THE BOOK, or somebody's book, maybe only my book, that's the perfect hand to stand. Which does you no worse than hitting to a bust and gives you the percentage to catch up. A loss. a push, a surrender keeps you pretty much out. And that's all I have to say about that, thaptszperbuzzitz.

 

Hitting better than standing but...

...Surrender is best. I think!

If you want to win the hand (rather than push) then hitting is better than standing. Standing you will win 16.7% of the time, hitting you will win 24.5% of the time. However I would surrender (and this is where I will probably come unstuck ) because the expectation is better. If you surrender your expectation is $5500, if you hit it's $2200, if you stand it's $1837. I'm not sure whether EV is a valid analysis in this situation but it's convinced me!

Cheers

Reachy

 

Hey Noman I use THE BOOK all the time - it's great for propping open the door, putting the laptop to see better even in the car for the little ones!

Yeah I use THE BOOK all the time! :joker:

PS Just when you thought it was safe to venture out on the forum boards.....

 

Hummmm

In my opinion, EV is not valid in this case. EV gives an average of your expectation if this hand is played over and over again. However, your gain/loss will never be at the average. To your bankroll after your bet, you will add $0 (loss), $5,500 (surrender), $11,000 (push), or $22,000 (win). I guess the real question is: Do you want to risk being almost knocked out by playing a hand that has a very low expectation of winning/pushing or keeping half your bet and have a viable chance to win on the last hand?

A loss keeps you pretty much out since you need a BJ with a ALL IN bet to have any chance. A push or surrender keeps you as a viable player because a BJ is not critical to be one of the top 2 chip counts after the last hand. Sure, you are the underdog but you still have a decent chance.

 

still not clear

It's not clear to my why EV isn't a valid analysis in this scenario. The other players outcomes are irrelevent so the only thing that Sabre has to do is maximise his outcome. How can we else can we measure whether 100% chance of 5500 is better or worse than a 24% chance of 11000? Please help a statistical noob!

Cheers

Reachy

 

Imagine an extreme case ...

Suppose a special rule were in force: If you draw an Ace of Spades, you automatically win the hand and get paid 100:1. Under such circumstances, hitting would always have a higher EV than any other option, but the probability of it winning the tournament for you is not worth factoring into your considerations.

What makes surrender a potentially attractive option is not the EV, that's just another way of saying it's the correct Basic Strategy move, rather it's that it guarantees your position going into the next hand; you can 're-invest' half your stake and put it to work for you in the next round (hoping for better cards).


It's an interesting general topic - basic strategy is all about maximising EV, but in the short sprint that is a tournament, rather than the marathon of all the hands of regular BJ you might get through in a lifetime, that may not be what you want.

Some DDs and splits reduce your overall chances of winning (and cost you twice as much when you lose); so unless winning two bets is important, it may be more prudent to disregard the normal BS.

Similarly, if you are an underdog in a hand, BS may say to hit or stand. You'll lose the hand more often than you win it, but not so often that surrender is the best option. In a tournament though, surrender becomes tempting.

 

Forgive my ignorance

Thanks for the explanation Colin and although I'm still not completely happy I understand, I'm getting there !

I get what your getting at with the Ace of Spades example; interested to know what the actual EV for that would be .

I also appreciate that one does need to deviate from BS during tourneys and I am especially wary of splitting and DDs.

On your last point, according to my quick mental maths, you'd need to have less than a 25% chance of winning before surrender became the best thing to do. Am I right or completely missing the point?

Cheers

Reachy

 

I'm no expert myself

Reachy,

I probably sounded more confident of my facts than I actually am in the above post. It represents my understanding of the issue, but I'd be happy to defer to those with more knowledge.

Assuming you're talking about the calculation of EV here, and not tournament-based decision making, then 25% does indeed equate to an EV of -0.5 (the same as surrender) if the only possibilities are to win or lose a single bet. The situation becomes more complicated with totals of 17 and above (where the chances of a push come into play), and also with pairs (where you can win/lose multiple bets by splitting and then perhaps re-splitting or doubling).

There's a useful (java) tool at http://www.gamblingtools.net/bj/ppbj.html. I plugged the rules used in UBT into it. The EV figures for 8,8 vs dealer T are most illuminating -

STAND: -0.5369
HIT: -0.5354
DBL: -1.0707
SPLIT:-0.4756
SURR: -0.5000 (As always!)

Ignoring the suicidal double, there's scarcely anything in it. What would be useful to know from a tournament perspective is how much of the gain in splitting comes from those occasions when you get a push overall (i.e. win one split hand and lose the other), and how much comes from winning both split hands. (Or, looking at it another way, what's the probability of losing both hands?)

 

You know more than I

Thanks again Colin (Do you remember a sit-com with Mel Smith called "Colin's Sandwich"?)

You're right, with the 25% example I was thinking simple win/lose.

16 vs T is one of the closest calls in BJ if my memory serves. There's hardly anything between hit and stand (as your figures show) and assuming surrender isn't available going one way or another will have a very small effect on outcome.

I'm still curious though as to how to compare surrender and other actions in a single tourney hand. Do we just go by straight percentages? If so at what point does hit/stand/double/split become better than surrender. You mention that in the scenario above that surrender is a way of minimising your loss to $5100 rather than the full $11000. So a 100% chance of losing $5100 is better than a 24% chance of winning $11000 is what you are saying. What if you had a 30% chance of winning $11000? Or 50%? Or is this the wrong way of looking at it? Is it about how a player views risk?

Cheers

reachy

 

It's all rather subjective, I think

In the run-in to an elimination or last hand, I'd say it is the wrong way of looking at it, or at least only part of the picture. What needs to be considered (and I'm terrible at this) is the various possible scenarios for the sets of chip stacks that everyone could end up with going into the next round, with some rough assessment of how probable each of them is. Based on the number of rounds remaining, some of these scenarios may put you too far behind to be viable. The unique feature of surrender is that you can at least be 100% sure of your own chip stack, but if it is too small then that certainty does you no good - surrender is the wrong option.

Often it can come down to a choice between extremes. If you are on 15 or 16 with a couple of rounds to go and a big bet out, the thought process may be -
"If I take another card and bust then I'm out of contention, so if I am going to do that I might as well DD and get full value if I should get lucky. Alternatively, if I surrender I won't be totally out of it and I could go all-in on the next hand. Hmm, what shall I do? Hmm... Oh bugger I've been timed out! "


There's a slightly more academic angle to this, more in line with the way you phrased the question :-
Even in the early rounds, when you are betting small and playing something akin to 'regular' BJ, should Basic Tournament Strategy be a slightly modifed version of normal Basic Strategy? By giving up a small anount of EV through declining to DD or choosing to surrender, you might gain a certain amount of predictability - narrowing the range in which your BR is likely to lie when the time comes to start vying for position.

I doubt the above is more than a curiosity though. I can't see it making much difference unless a tournament consists of a very large number of rounds (with no elimination rounds along the way).

 

This is why I love TBJ

OK. If BR3 surrenders in this situation they are, even if BR2 loses, greater than 1/2 max bet behind. This means, as you know, that BR2 can take the high and the low and still beat a BR3 push with a loss. If BR3 hits/stands on his 11K and loses he's going to be 20K behind. Is that a much worse position? It's worse but I'm not sure BR3s chances of winning with that deficit are much worse than with a deficit of 13K. As usual I'm not completely sure about it and I'd be interested to know what the odds are for either scenario if any of the maths whizzes are reading this post. And of course the upshot of hitting is that you have a 1 in 4 chance of winning your bet and becoming BR1.

What do you think?

Cheers

Reachy

Ps. Have you played cash games in any UK casinos?

 

It may be quite close, but I think surrender has it

I think the clincher in favour of surrender is that it leaves both BR1 and BR2 in range. A swing against either one in the last round will allow BR3 to advance.

There's a 0.70 chance that at least one of them will lose/push the last hand. Combine that with the 0.44 chance that BR3 wins and you get a 0.31 chance of advancing.

With only one opponent to swing, the probability is only 0.14. (But to this must be added something to account for the possibility of overtaking them both this hand, and then going on to stay BR* after the next hand. i.e. not getting overtaken by both yourself)

Since 16 vs A is a BS surrender, the probablity of winning it must be less than 0.25. Once the further conditioning relating to the outcome of the last hand is factored in, I suspect the final figure will be lower than the 0.17 needed to match the surrender option (i.e. a 0.17 chance of advancing through winning this hand, plus a 0.14 chance of advancing despite losing this hand would equal the 0.31 chance of advancing after surrendering this hand).

 

Give yourself more opportunities to win

Reachy:

From your posts on this subject, it seems to me that you are missing the concept here. As stated by Joep on numerous occasions, you want to give yourself as many opportunities to win as possible. Keep in mind that we are talking about the second from last hand and BR3's bankroll puts him in a very bad position. He must optimize his chances of being successful over a period of just 2 hands. He does not have the luxury of using EV which would be OK if there were many hands left.

Now let's get to one of your questions:

Again, give yourself the best opportunity to win. When you are "behind the 8 ball" you just have to do the best you can given that there are only 2 hands to play. BR3 can still advance but only if he gives himself the opportunity.

 

UK Casinos

I've ventured into exactly four UK casinos.

I'm very much a 'low roller' and the problem with living in London is that the min bet seems to be £5 everwhere (and many insist that you play two spots if you are alone at the table). I joined a Gala casino in London, but once I discovered these facts I wasn't inclined to play very often. I wanted to try out my counting skills, but with the poor rules we get in this country a spread of 1-10 or 1-12 is recommended, and I don't like the idea of betting £60 on a single hand of blackjack. With so few tables, Wonging is not really feasible either. You'd have to keep leaving and returning to the same table, which would make you very conspicuous and would also mean you got through very few hands per hour.)


Elsewhere in the country, £2 seems to be the norm. I discovered that there are three casinos in Southend within walking distance of each other. For less than the price of three London min bets I can get a return train ticket and be there in about an hour. One is operated by LCI and the other two by Stanley Leisure (they are really the same place; there's even a connecting door).

However, I was surprised to find that the Stanley casinos operate the H17 rule. I had thought all UK casinos were required to use the same standard set of rules. At any rate, that only leaves one casino (with just two low-stakes tables) where I would currently consider playing.

Of course, the Millenium Dome is just down the road from me, so I look forward to the arrival of the 'Super Casino' (assuming that the deal has been sown up, as everyone suspects).

 

Concept

Thanks Toolman for your response. I do understand the concept of giving yourself more ways to win, I'm just trying to get my head round how to decide what's the best way of achieving that. I do now understand why EV isn't a usefull measure in this scenario so we're getting somewhere . Infact I'd moved on from that in my last post when I was asking whether BR3s position after an 11K loss was much worse than a 5.5K loss. Even if BR3 did lose the 11K he could still swing both BR2 and BR1 as even if BR1 wins his 500 bet he would still only be 21.5K ahead. A bet on the final hand of at least 22K would beat a lose or push from either BR2 or BR3 which as far as I can see gives the same odds as if you were 16K behind the leader. Surely then by hitting the 16 with the admittedly very small chance of winning gives you more options to win because your postion if you lose is not worse than if you surrender but you could be BR1 on the final hand?

I realise I may be flogging a dead horse here and I'd be happy to admit to being wrong if you can convince me that a 21.5K deficit is a much worse position than a 16K deficit. But if you accept that both BR2 and BR1 can be swung from either position don't you in effect have a "free hit"?

Cheers

Reachy

 

Maths error

Tricky to do when you only have 20K

 

Fatal flaw

LOLOLOLOLOLOL!!!!

Thanks Colin! I knew I must be missing something here. Wood for the trees and all that.

However, add 50K to everybodies BR (i.e. BR3 - 81K, BR2 - 89K and BR1 - 91K); would that change things?

Cheers

Reachy