On Saturday I was playing a blackjack tournament at the Cal-Neva against a whole bunch of other players. The top 10 players for the day get to advance to the semi finals and you are playing against all tables in the tournament not just your own table. Plus there was a wild card drawing for another 5 players as a gimmick to keep the players in the casino. I played the last round and the 10th place player was about 9,000 chips for while the top player had 12,800 chips the middle of the pack had 10,800 for the leader board. The top 10 for all 5 rounds which had about 8 tables of 6 players in each round where the only ones that got to advance so more players could push the minimum advancing bankroll higher in the last round. The rules for the tournament where as follow each player starts with 1,000 chips, blackjacks pay 2 to 1, double any two cards, double after a split, minimum bet 25 chips max bet 1,000 chips, the round is 25 hands of blackjack or until you bust out no re-buys. Prizes where $7,000 for first $2,000 for second and a $1,000 for third 4th place $700 of action chips and 5th place was $500 of action chips. Buy in was $39 I got it comped. My strategy for the tournament was to bet the max on the first hand and I lost. Was this the right strategy mathematically? If I would have won the hand I would have kept on betting the max until I hit 11,000 or 12,000 in chips than I would have bet the 25 chip minimum for the rest of the hands. I bet the max because finishing the day with 8,975 chips or less was equal to finishing the day with zero chips in my mind.
Odds Although $5,900 to $6,000 should normally advance you to the top 10 with the bankroll and number of players stated, 2/1 blackjacks makes this a + EV game so your final $ goal must be increased. Playing in the last session of round one and knowing other players prior winnings makes a prior determined $ goal obsolete. Your $ goal with this knowledge is now as you indicated. Your strategy of betting maximum until your $ goal is achieved is correct based on accepted "Accumulation" format blackjack tournament strategy. Bet max every hand until you achieve your $ goal or go broke.
Yes, but.... I thought Wong had a progressive calculation for accumulations, wherein you didn't necessarily bet max first bet. I personally don't care for accumulations, so I don't follow, know or even care about the exact formulas. But the "Thang" was rattling around in the back of my head, so I thought I'd throw it out. Good Fortune.
The casino had the top 10 scores posted already 10th place had 9,000 first place had 12,800 for qualifers into the semi finals it doesn't matter if you finish 10th or 1st. Just as long as you are in the top 10. 9,000 I knew would not cut it on that day. 5th place was 10,800 I wrote that number on a piece of paper because that was kind of my goal.
noman Wong's theory to achieve a $ goal in accumulation tournaments to advance is definately not a progression betting system but remains to be refined as published in my opinion. His formula published in CTS chapter 3, for a $ goal to reach the semi-final table includes many options including whether you are counting cards or not which I won't address as tournament strategy, pro or con. His general published theory is; Number of participants divided by number of participants advancing, square root this number X starting bankroll = desired $ goal to advance. I take exception to Wong's generality as it does not take into account, maximum bet vs. bankroll. My experience indicates in both Baccarat and Blackjack accumulation tournaments this formula is accurate when the max bet equals the starting bankroll but extremly inaccuate if the max bet is less than the starting bankroll, i.e, starting bankroll $25,000, max bet $5,000.
Accumulation Strategy Wong's formula is just a badly bastardized way of estimating the standard deviation. If you have some math you can do a better job of identifying resonable goals. The key to accumulation play is reaching your goal in as few hands as possible. I am not sure if EV is as relevant as the fact that you will win fewer hands than you lose, regardless of EV. So, your better off betting extremes, bet the max possible for as few hands as possible til you hit your target, then bet minimum. That maximizes the probably that you will reach your goal before bankrupting out. But tournament rules can change your approach. At the Tropicana in Laughlin, in their accumulation tournaments, you could go all in on the last hand, so the correct strategy was to max bet until you reached one-half your goal, then bet minimum until the last hand - when you go all-in for the double up. With 25 hands, you might want to count, especially if they were using single deck or double deck.
What are the odds to turn 1000 into 11000? Look at it this way. You need to have a net gain of 10 max bets. In 25 hands on average you will have 2 pushes. That leaves 23 decision hands (W/L) to gain 10 bets. If you win 16 and lose 7, you will gain 9 bets. There is between 5-6% chance of this scenario. You have about 2/3 chance of having a BJ in 23 hands. That would give you your extra bet to get to 11000. You also have the possibility of DDs and splits to gain the extra bet(s). If you do not start off betting the max and keeping after it, you will be reducing your opportunity to gain 10 max bets. So go for it. Larry
RKuczek, It appears we agree in Accumulation tournaments max bet each hand until a goal is achieved is the best strategy. You stated "If you have some math you can do a better job of identifing reasonable goals". Can you expand on your "math for a better job identifing a reasonable goal" theory other than the Laughlin example of all in the final hand, you've left us with a philosophical yet unanswered equation. Please explain your math (formula) to achieve a reasonable $ goal in accumulation tournaments that differs with Wong.
For Discussion: And a great one in this thread. I generally agree with Rook, in the distinction between starting bankroll and max bet. I took the initial post as "going all in" from the get go. But, again as I interpret the Wong formula, it is a progression of your starting bankroll, after you've determined your goal and perhaps seeing earlier round totals. Whatever method one uses it is to reach your goal or bust trying to. Again though, I have no dog, or goat in this "fight."
The Laughlin example was just pointing out that in the specific case where there was a max bet, but, you could go all in on the last hand, your best chance of reaching the target wasn't to bet until you got to the target, but, bet until you got to 1/2 the target, then minimum bet and go for the double up on the last hand. Better odds of winning one hand (the last) then a series of hands. Go to any basic stat book and look at the formula for calculating the standard deviation, then look at Wong's formula for calculating accumulation targets. Pretty obvious that Wong is trying to come up with a formula, based on standard deviation, that can be converted to a target, and applied across many formats and situations, i.e. badly bastardized. That's where Wong's formula can go very off. In Example, in the Tropicana-Laughlin tournaments, you combined your totals in two rounds, but, you also had the option of doing a rebuy round, and then you would use the best two out of three rounds. This is the kind of situation where Wong can skew way off. Likewise, trying to come up with a simple equation that would deal with no max bet, max bets, last hand all-ins, single round totals, two round totals, best two of three round totals, etc. without alteration, pretty much guarantees inaccuracy in every situation. If you want a formula - simply go to any basic statistics book and find the formula for calculating standard deviation, and work from there. That assumes you have some knowledge of probability and statistics, and feel comfortable doing such an analysis. What you need to get at is the number of hands won that would be an 50% chance of being at the final table. You could also use the Chang Bioscience probability calculator, readily available on line. Rough example: using the Chang Bioscience probability calculator: Say, 125 players, one accumulation round, 7 at the final table, 25 hands. 7/125 is 0.056, winning 15 hands or more out of 25 is a 0.0724 probability, winning 16 or more a 0.031 probability. So the top 7 players should win at least 15.5 hands, meaning they will win 6 hands more than they will lose, so a reasonable guess is that the target for reaching the final table (50% chance) would be the starting bankroll plus 6 max bets. So, if starting bankroll is $2,500, and max bet is $1,000, target is $8,500, to get a 50% chance at reaching the final table. This approach can be adapted to other formats, such as the one used at the Tropicana-Laughlin, but the reasoning and calculations start getting more complex. Obviously you can adapt this approach to provide a higher percentage of probability to reach the final table. Doing some simple calculations, using normal probabilities, real standard deviation, etc. will give a much more accurate target than Wong's formula, but takes a little more work; if you have odd formats, rules, etc. then you need to be enough of a mathematician to adapt and handle a more complex analysis. But you will get a pretty accurate target for the specific tournament you are analyzing. Better than Wong's formula gives you. If you can't work with the math, then go with Wong, but give yourself a big margin for error.
Rk I've attempted to make this an apples to apples conversation but you continue to make this an apples to oranges comparison, including personal deregatory comments such as "If you can't work with the math". My original post was in regards to CardCounters question regarding making a max bet until his goal was acheieved which in my opionion and experience is accurate notwithstanding additional information not provided. We both agree Wong's accumulation standard formula as publiblished is not 100% accurate due to deviation of rules in idividual tournaments such as your Laughlin example but I ask you submit your simple superior to Wong's formula for a two round, advance to semi-finals accumulation tournament excluding the Tropicana Laughlin or other casino abnormal tournament rules you've experienced which are evidently local. Wong did not try to cover any and all options in this or any other chapter in his book, your criticism is well admired if you thought the purchase of CST would lead you to absolute success in tournament strategy but it's simply a guide for basic tournament strategy, not a bible for ever lasting life. Wong's formula agreed did not include options such as an all-in bet last hand, 2/1 BJ's or 5 card charlies you evidently included in your opinion of his "Basterdly" Formula, lets agree Wong's formula is X% accurate as suggested for a normal 2 round accumulation tournament prior to the semi-finals or make proven mathematical accusations relevant to the opposite. I have "The Math" as you suggest as an engineer but request you prove your theory as suggested rather than ask me to disprove your theory based on multiple hypothetical circumstances.
