Disclaimer: Before you read this thread I'd like to apologise for it! It is at best confused and at worst the mutterings of a madman! As I was writing it I kept on changing my mind about things and tried to correct what I thought were obvious errors (many of which are still there). Please be kind and appreciate that I have become a little obsessed Hi Guys Since the “Is there a BEST bet” post I’ve been thinking about the application of Table 4 in Wong’s CTS (Pg 131) and as you might have guessed I have several questions related to it!! First off, how was the table 4 data generated? I’m guessing simulation. Before I knew about the table I guessed the probability of 2 players beating the dealer was 0.44 x 0.44 = 0.1936. Table 4 says it’s 0.30. I realise this discrepancy is because both players are likely to have a similar outcome versus the dealer. If table 4 was generated with simulation data has it been verified by others recently? I’m sure I’ve heard in other threads that some of you doubt the accuracy of Wong’s numbers. Is there an expanded version of table 4 available that includes data for double downs, both basic strategy related DD and forced DD (i.e. DD in the last few hands which may go against BS but are required to get more money out). In the “Surrender Trap” thread S. Yama said that the probability of a win from a forced DD was 0.31 but is there anything along the lines of “Player A wins forced DD, Player B wins”? In “Is there a BEST bet” I suggested what I thought the best bet was and using Table 4 data MonkeySystem showed that there was a better bet than the one I proposed. He demonstrated that my bet was at best 50:50 whereas his bet was more in BR1s favour. The question posed was… 2 players left one advances Br 1 bets first has 327.50 Br 2 bets second and has 252.50 No cards dealt at this time. So what is the definitive bet here? I suggested 305 to cover an all-in win by BR2 and MonkeySystem suggested 145 which is better because it forces BR2 to win his hand to have a chance of beating BR1. Since we know that BR2s chances of winning are only 0.44 it’s already obvious that the 145 bet is better than 305 plus BR1 can surrender and DD if required which further eats away at BR2 chances. What I wanted to do was calculate exactly the probability of a 145 bet winning and have hit several obstacles. Firstly, there is no data for doubling down in Table 4 so I had to approximate a value and I’m not sure whether it over or underestimates the actual probability. Secondly, when do you surrender or DD when acting first? Again, I know that MonkeySystem has dealt with the surrender side of things before in a previous thread but I can’t seem to find it. My thoughts are that you should only NOT surrender when BR2 is more likely to win than lose (or surrender when BR2 is most likely to lose). If he is likely to win then you need to win a DD. But this is further complicated by the fact the probabilities change once the cards have been dealt (Schrödinger’s cat anyone?). If for example you both get dealt 20 and the dealer is showing a 6 what do you do? BR2 is likely to beat the dealer (0.80 minimum) but you need to DD to beat BR2 and you are only going to win that one 0.08 of the time. I guess it’s actually an easier decision than I initially thought; you have to stand and hope that the dealer gets 20 or 21. So the rule here might be DD only if you chances of success are better than BR2 losing. So how do I figure the probability out? Is it possible or does it need to be simulated? Well here’s my stab at it, full of holes no doubt, but at least if they can be pointed out I’ll be happy . I’ve used a bet of 225 by BR2 which may in itself not be the best bet but it does cover a single bet win by BR1 and an all-in bet offers no extra value as far as I can see. Assuming BR1 plays whatever he is dealt perfectly and surrenders and doubles down when that is the best thing to do I believe that he has a 0.7 chance of winning the hand. That is if BR2 beats the dealer BR1 needs to win a DD = 0.44x0.31=0.1364 (this is the most obvious weak spot in the working out); if BR2 loses then any outcome is acceptable for BR2 = 0.48; if BR2 pushes BR1 surrenders = 0.08 which when all added together makes 0.6964=0.7. What so you think? Am I miles off? Do I need shooting? Also as I was examining the problem last night I realised that the problem looked very similar to those dealt with in Game Theory. I have at best a very rudimentary understanding of game theory and I wondered whether anybody has looked into this avenue of investigation in more detail? Cheers, thank you for humouring me and send any spare medications you might have! Reachy
Blew you away didn't it? C'mon guys, tell me what you think. Which end am I talking out of? Cheers Reachy
I don't have a nice handy shortcut to do these calculations. Instead, in the past I've used simulation, on a case by case basis. (And most of the time, that means I don't bother!) I'm working on a software project that will easily answer these questions, but it's not there yet. I can point out a reason that $245 is a better bet than $225 behind BR1's $145. A BR2 blackjack beats a BR1 double-down in that case. Hey, if I can't answer the real question, I'll answer another one instead!
Hell's teeth My brain was very fried by the time I got to thinking about what BR2 should bet and I suppose for the purposes of this "investigation" it didn't really matter too much, but that's just an excuse. I hate it when I miss the most basic things. I guess then that these sorts of problems can only be solved with simulation? Another thing I noticed when looking at Table 4 was that for 1 and 2 players the probability of all players winning was less than their probability of losing which is logical. However for 3 or 4 players the probabilty of them all winning was greater than them all losing. How can that be? Cheers Reachy
All or one Reachy, I don't have my book to check your reference, but is it odds of at least one beating you or all beating you? It makes sense that the more people who have a shot at you, at least one will probably do so. It makes less sense like you have noted for everyone to beat you. Pat
all win or all lose I've just got the book out... The probabilites are vs. the dealer One Player Win 0.44; Lose 0.48 Two Players Both Win 0.30; both lose 0.31 Three Players All Win 0.23; All lose 0.22 Four Players All Win 0.19; All Lose 0.17 I can't understand logically why this (more chance that all win vs. all lose when you have 3 or more players) should be the case and is why I'm concerned that the simulation that generated this table is dodgy. Wongs tournament software is pretty much slated from what I've heard so I'm really not confident about any of the numbers in his book, not just this table. Cheers Reachy
Interesting anomaly. Here's a possible explanation... All players are likely to win together when the dealer has a small card up. They'll all stand, and all win together if the dealer busts. This is apparently more likely than all players losing together.
I can dig that Sounds like a reasonable explanation Ken. A lot of players seem adopt the minimum bet approach early on and of course Wong advocates it, at least initially. Do these win:lose anomalies when more than 2 players are in contention affect that rationale at all, if in fact you think it is a valid appraoch in the first place? I am personally rethinking my early betting strategy and I wondered whether this might have any bearing. Has anybody verified Wong's Table 4 data or any other data from CTS? He doesn't specifiy how he got the numbers, how many hands were involved in the simulation etc. Or do we have to wait until your book ? Get it published Ken before I explode!! Cheers Reachy
First you need to remember that these numbers would apply only in the early phase of a tournament round where most players use approximation of basic strategy. The reason, which may seem not obvious to you, that with three or more players chance of all of them winning against dealer is greater than all of them losing is a composite of all situations. But worth noting are couple facts: all players playing no-bust when the dealer shows a small card win if she busts, and also sometimes they all win when they have better pat hands than the dealer making a hand. Then, when she ends up with a good hand, all players individually take shots at beating or pushing the dealer, so at least one of them will not lose. S. Yama PS Ken was faster responding, giving the answer that shows one of the reasons, but all players winning when the dealer bust is not enough, it is countermesured by all of them losing when the dealer makes a hand, which happens (making the hand) more often than not.
Reachy, Having arrived only recently to the world of BJT I have made some interesting observations or my own play and the play of others. What is very interesting is the playing styles observed at three different sites, Global, BJ21 and AOL. My own personal observations: Global players - very conservative and follow the minimum bet approach early - few early busts and play usually comes down to the last 5 hands with extensive betting strategy playing a part. Most players use basic strategy until the final few hands BJ21 players - more liberal in their approach very few minimum initial bet players with higher betting involved. More guests busting out earlier but level of play usually coming down to the last few hands with betting strategy prevailing. Basic strategy in most instances observed. AOL - whoa nelly! All over the board some minimum betters, some max betters very erratic play - especially during first round. In the later rounds a little less chaotic but higher level betting in general with a departure from basic strategy prevalent. Why do I say these things? An early betting strategy that works in one format may not work in another format. Minimum betting on AOL in rounds 1-2 can usually get you a seat in round 3 (other players all bust out) However when the dealer is running cold the lead these other players surmount may be too much to overcome. Minimal betting on Global will likely get you to hand 13, however I find myself at a distinct disadvantage at that point due to my experience levels versus the long-time BJT players that I have encountered. What is my point? With so few resources available (at least in print) and the interest in TBJ likely to be spiking (thanks to UBT and TV) maybe it is time to re-think the early betting strategy. Remember when you follow the herd all you do is step in their droppings! Know where the herd wants to get and get there first! Ken, is that manuscript done yet? I would hate to see Sir/Barron Reachy splashed all over the site when he explodes
What's the BEST bet? Interesting stuff fgk42 and I agree with your observations although I have yet to play an AOL tourney. I wonder whether part of the reason why players on bj21.com seem to use more non-minimum betting strategies is because of the play money games they offer? Just a thought. I guess the principle behind minimum betting is to preserve your BR until the final few hands and then put some big bets in then. In the era of internet gambling where lots of players adopt more aggressive strategies, playing many games at once, where it often becomes a number game, I wonder whether TBJ players are going to have to rethink their approach. A lot of the top poker players now cut their teeth online. No reason to think that the same won't happen in TBJ. These recent posts on accumulation tourneys have got me thinking as have the old chestnuts like progressions. I know that elimination BJ and accumulation BJ are very different beasts but in the early stages at least are they not quite similar? Food for thought (for me anyway!) Cheers Reachy
Reachy, Your observation about BJ21 and having the free and pay games together may explain the "loose" betting. I however believe that the players at Global are more experienced/savvy/"old school". I've chatted with a lot of players at BJ21 and a majority seem to be like myself, familiar with BJ but not TBJ - it is a new entity hence the unfamiliar betting styles. In the long run the more people use the minimum until the last 5 hands the more difficult it will prove to be to distinguish oneself in the long run. Accumulation vs. TBJ is a whole different beast and I would love to read the seasoned members advice on that subject.
