All-In, Three Advance, You're First

what to do?

Bet 500.00 providing the ability to split or double, depending on the dealers card, and the bets and cards of the other players.

 

My Opinion

I have the old Stanford Wong Tournament Play program. I believe it has insurance built into it and I do not know how to turn it off.

I ran simulations for $25 vrs $500 and $25 was far superior. I then ran $25 vrs $50 and after a few thousand iterations. They were only separated by
.004 so it is inconclusive.

I believe you just fall back on the "take the low" and hope that 2 people below you do not win. Even if they do, you may actually go ahead of the leader if he/she loses.

As the intial bettor on this scenario, I don't believe it is going to have much of a significant difference whomever your competitors are.

Larry

 

You cannot take the absolute low because BR1 has more chips than you and may take the low. If you take the high(OR 2ND high) you must win your bet, 48% probability,leaving at least 4 and possibilly 5 players to take the low end. I think a bet of 150 might be sufficient, as it means that 4 of the five players must beat you-- assuming you win-- and all of them must bet at least 25. I also think that once you make your bet that 4 of 5 players realize that they must make a bet larger than yours if they are to win.
Taking the low ---or 2nd low--- gives you less options than a moderate bet of 150.
I guess some of our "CEREBRAL STUDS", (been wanting to use that term , sounds familiar doesn't it?) can take a whack at this teaser and arrive at a better wager, but with time constraints, disadvantage of 1st bet, and the number of options available, 150 seemmed to be a good bet.

 

I deliberately stayed out of this one for awhile because Monkey and I had already talked about this teaser before he posted it.

Even without any of the computerized analyzers, I liked the minimum of 25 best. With three advancing, two of the four trailing bankrolls must win their bets to knock you out, putting the advantage in your corner. Plus there is the much more minor consideration that you could DD to get over BR1's push although that scenario is unlikely.

There's also the consideration of what might happen with the betting behind you. One (or more) of the 4 lower bankrolls might also bet very small, taking them out of consideration for betting enough to blow past you.

 

Monkey, Left Nut,
I like the 25 bet, and it may be the best bet, but I also would like to bet my lead over the 4 bettors below me. My 150 bet may trigger the 4 lesser bankrolls to bet more than I, giving me the 1st or 2nd low. 150 also gives me a few more options.

 

I was trying to think along those lines, in search of some insight. I decided that BR1, acting in Spot 2, might give up the low to you, rather than correlate, if correlating would allow three of the remaining four players to take the high. I think he might want to cover an all-in win of 1800 by Spot 6, which means an 800 bet for BR1.

I therefore reasoned that any bet <= 750 might give us the low against BR1. (And a win of 750 would tie with an all-in win by Spot 5.)

I sort of ran out of steam at that point! 25 may well be the best bet.

 

Speculation

You bet 25, 2nd spot bets800 to cover an all in by spot 6. I think spots 3 and 4 will bet the same, both high or both low, leaving 5 and six to bet the opposite.

I believe the betting order will be 3 high and 3 low. If this is the case, then you are in a better position with the low.( I took some liberties here and used Wongs table 4 pg 131 where 2 of 4 advance)

With all the variables involved in this teaser, I doubt that the optimum bet (whatever that is) will be placed frequently.

It has been interesting.

 

With average players

In a situation as described many average players like to bet big. If the dealer gets a low up card and eventually busts (average players play basic strategy), then all those players will pass a $25 bettor. I don't think a $25 bet is good. I like to bet bigger when in doubt.


......................BlueLight

 

3 Advance, All in, Wong's Tournament BJ Program

I never posted the %'s I was getting using the program simulations, because I didn't initially like them. However, after a suggestion from Ken (thanks), I like what I am getting better, but see the caveats on the Tournament BJ program below. But first some %'s for first player

Bet 25 - 54% advance rate.
Bet 50 - 53.6% advance rate.
Bet 1000 - 50% advance rate. Reasonable, with a 44% win rate and will advance most of the time on the 8% push hands. Since, dealer will have had to make a hand and the other players have to have at least one more than dealer to win.

I am making the following assumptions that player 2 will not give up the low and will match player 1 up to 50. The low four players will bet at least enough (usually all-in or close to it) so if they win they will blow by the first 2 players. The last player normally will be taking the 3rd low (if available and no other option) having the positional advantage. I did look at the situation where one of the last 4 players tries to just bet 25 and it pushed the first player's % up to 60%. On most scenarios that I looked at the 2nd player had the % advantage, but the 6th player often has the % advantage over the others.

Caveats on Wong's Tournament BJ Program:

I have had this program a long time probably 10 years or close to it (could only get in floppy when I bought it). I did not use for many years.

It has insurance built into it and I can't turn it off. So over the long run, 1 in 13 hands the dealer will have an Ace up. I do not know what the program does on these hands in simulation. I am assuming that if the 1st player takes insurance then the 2nd player will match. I turned off card counting so the program will hopefully not take that into account.

I do not know what the program does when the 1st player ties for 3rd. This would normally be with the 2nd player and I don't know how it allocates the % involved.

I do not know how aggessively the program plays the hands. Does it take any action to advance?

If you have this program, in any multiplayer scenario you may want to run your bet simulations with the last player. If you have a scenario, like this one, and try to use the first player's bets for your simulation, the program generates what it considers best bets for the other players. These are not necessarily the "best bet". I found this out when I was looking at this scenario.

Larry

 

three advance

Larry, here is my promised and long delayed –sorry- response.

Last hand, three advance.
You, bankroll 1,000, bet ?
Spot 2, bankroll 1,025
Spot 3, bankroll 925
Spot 4, bankroll 950
Spot 5, bankroll 875
Spot 6, bankroll 900

At the tournament table, with limited time and under pressure, as BR2, I would be tempted to bet 50.
Betting 50 is somewhat better than betting 25 (contrary to Wong’s simulation) because if you were matched by BR1 your blackjack or winning double bet against BR1’s single win, and your win while BR1 pushes, gives you advancement if only two out of the other four remaining players win their bets.
Given time to think about it my thoughts were very similar to those of Monkeysystem, firstly contemplating about how often BR1 would correlate my different bets. I would guess – very often, but this is not that crucial in this case.
If you bet small there is practically no chance to have a “high” – with BR1 likely matching your bet you will have to have three out of four players lose/push, or swing (gain) the leader and two other players push/lose. It gets slightly better if BR1bets high. My guess is that even if you assume equal chance for BR1’s matched and a big bet your chance of advancing would be just below 50%.
Bet of 925 would be a good “high” bet; almost guaranteed to be matched by BR1. You advance when you win (short of two or three blackjacks and BR1’s win) and most of the times when you push. But more importantly there is a good chance that BR4 (bankroll 925) will bet all-in (not a bad bet). Then you need just one more player to bet almost all-in, a common tendency for less experienced players, giving you third/second low and second high, thus additionally increasing your chance to advance, even when you lose, by about 25%.

I rarely use terms first low, third high, etc., because they are usually difficult to quantify. Most tournament players realize that tournament play differs so much from basic strategy (bs), and using data for bs plays would be considerable off. For example, gaining over two other players and having playing position on them will be much higher that basic strategy play would show, because she or he would know to hit until at least one point over the best result of either one of them. Overall optimal tournament strategy correlation tables can be calculated but there will be many of them as number of opponents and number of advancing, and each position and different position configurations produce different statistics and tables.

As to Wong’s program you said: I do not know what the program does on these hands in simulation – exactly, I don’t know either. My early version had also some bugs and would give wrong answer to straightforward problems that I could relatively easily check using combinatorial analysis. It would be fun to see exact result that you could rely on and if you could input particular players betting/playing tendencies – but that would have to wait until somebody who understands tournament blackjack get onto it (Ken any free time to work on it?). Meanwhile it is so much more productive (and fun, at least to me) to spend time looking for all intricacies of situational relations trying to distil broad and general ideas, isn’t it?

S. Yama

 

I know this thread is old, but hopinglarry asked me to re-run some of the sims in this thread in an attempt to confirm or refute the findings. In reading the thread, there was some concern expressed about not knowing how Wong's software handles certain situations. Using my own software, I can control those factors.

There were a variety of bet proposed, however the ones that sims were run for were 25, 50 and 1000. Of course the results depend on how the other players react. I tried to stick to the original assumptions:

Each simulation was 2 billion hands with the following rules: 8 decks, S17, DOA, DAS (except aces), SP4 (except aces), blackjack pays 2:1, no surrender, no insurance, double for less allowed. All players play basic strategy. Since being tied for 3rd has value (playoff or other tie breaker), the simulation considers being tied for nth place as finishing in nth place.

So, let's get to the results!

1) Betting 25
The actual bets used for this scenario are:
Player 1: BR: 1000 Bet: 25
Player 2: BR: 1025 Bet: 25 (matches player1)
Player 3: BR: 925 Bet: 225 (beats player 2 split with 2 doubles)
Player 4: BR: 950 Bet: 225 (beats player 3)
Player 5: BR: 875 Bet: 325 (beats player 4)
Player 6: BR: 900 Bet: 150 (takes 3rd low)

For these bets, the results for player 1 are:

Player 1 finishes: 1: 6.86% 2: 29.05% 3: 20.60% 4: 17.41% 5: 11.57% 6: 14.51%
Player 1 finishes 3rd or better 56.51% of the time, which is close the the 54% computed by Wong's software (caveat: only a few thousand iterations). The 56.51% number would be slightly lower if being tied for 3rd was not considered to be 3rd (tie breaker handling would make a good addition to my software).

2) Betting 50
The actual bets used for this scenario are:
Player 1: BR: 1000 Bet: 50
Player 2: BR: 1025 Bet: 50 (matches player1)
Player 3: BR: 925 Bet: 325 (beats player 2 split with 2 doubles)
Player 4: BR: 950 Bet: 325 (beats player 3)
Player 5: BR: 875 Bet: 425 (beats player 4)
Player 6: BR: 900 Bet: 250 (takes 3rd low)

For these bets, the results for player 1 are:

Player 1 finishes: 1: 6.61% 2: 28.31% 3: 20.49% 4: 15.98% 5: 13.37% 6: 15.24%
Player 1 finishes 3rd or better 55.41% of the time. Again close to the 53.6% computed by Wong's software, but more notably, both simulators computed an overall result which is lower than that achieved by betting 25. The probabilities of finishing in positions 5 and 6 are both higher at the expense of every other position. I suspect that this is due to increased exposure to pushes by players 3, 4, 5 and 6 via doubling and splitting. This result would likely be improved if player 1 doubled or split only when necessary to beat player 2.

3) Betting 1000
The actual bets used for this scenario are:
Player 1: BR: 1000 Bet: 1000
Player 2: BR: 1025 Bet: 1000 (matches player1)
Player 3: BR: 925 Bet: 875 (takes player 2 low)
Player 4: BR: 950 Bet: 875 (match player 3)
Player 5: BR: 875 Bet: 775 (takes player 4 low)
Player 6: BR: 900 Bet: 775 (match player 5)

For these bets, the results for player 1 are:

Player 1 finishes: 1: 16.43% 2: 26.74% 3: 6.50% 4: 1.66% 5: 2.14% 6: 46.53%
Player 1 finishes 3rd or better 49.67% which is very close to the 50% computed by Wong's software. The situation here is much simpler. I player 1 wins, he advances. If he loses, he doesn't. If he pushes, he still has a chance.

I simulated another scenario, suggested by S. Yama:

4) Betting 925
The actual bets used for this scenario are:
Player 1: BR: 1000 Bet: 925
Player 2: BR: 1025 Bet: 925 (as suggested)
Player 3: BR: 925 Bet: 925 (as suggested)
Player 4: BR: 950 Bet: 925 (match player 3 and close to all-in, as suggested)
Player 5: BR: 875 Bet: 750 (takes player 2 low)
Player 6: BR: 900 Bet: 750 (match player 5)

For these bets, the results for player 1 are:

Player 1 finishes: 1: 17.44% 2: 26.00% 3: 7.58% 4: 22.58% 5: 18.07% 6: 8.33%
Player 1 finishes 3rd or better 51.02% of the time.

Not the extra 25% that was expected. S. Yama, did I get the scenario wrong? The main effect seems to be that, by not going all in, the chances of being last were spread out among the chances of finishing 4th, 5th and 6th.

To Summarize:

The results of my sims are in the same ballpark as the results produced by Wong's software, with the caveats hat we don't know how Wong's software handles certain situations and that only a few thousand iterations were run using it.

The results would all be improved if player 1 doubled and split less often than called for by basic strategy; i.e. reduce exposure to pushes by other players when betting low; play to win the hand when betting high.

 

3 advance

Thanks for doing this. I am pleased to see that the Wong program wasn't too far off. I did also have to simulate off the last player instead of the first which anyone using the Wong program should consider if multiplayers.

Realistically this scenario just will not come up at Winstar, but if something similar did come up it looks like just taking the little bet is best. When I played a couple of weeks ago, unfortunately they will not allow anyone to bet early. They just push the money back and the person can bet anything they want when their turn comes. Too bad, it might make it a lot easier to pick that middle ground bet if you are early in the betting order.

I got interested again, because I was in the top 24 for one of their qualifiers and get to play in the 10/9 tournament.

Larry

 

Gronbog and all,

I was not clear with what other players had to bet. I wrote:
“Then you need just one more player to bet almost all-in, a common tendency for less experienced players, giving you third/second low and second high, thus additionally increasing your chance to advance, even when you lose, by about 25%.”
I also wrote of BR4 betting all-in $925, which I assumed would likely be followed by BR3 (brl $950) with a matching bet. That leaves one of the two other players having to bet big (keeping back less than $75). This scenario gives us (BR2) third low. To have second low (and BR1 matching our bet) all other players have to bet big and keep less than $75 unbet chips.

If BR2 is given second high and third low all three players that keep back less money than him have to lose. We’ve already got the numbers for advancing when winning or pushing so we need to find BR2’s additional chances when he loses. That means BR2 and all three opponents have to lose and according to Bluelight’s table this happens 16,8% of the times.
BR2 can increase his chances by modifying his play from basic strategy to increase the correlation to the other players.
The other players could increase their chances of swinging/gaining to BR2 by departing from basic strategy, but since they also aiming for gains among themselves it comes with increased chance of busting and all of them losing.
Additional chances of BR2 advancing, given third low, should be between 17% and 18%.

When BR2 is given second low his additional advancement when he loses comes when three out of four opponents lose. We are looking for BR2 lose and the other four players result W(win)-L(loss)- L-L, or P(push)-L-L-L, and L-L-L-L including all permutations.
Since I don’t have simulators I rely on understanding correlations.
The correlation increases with predominant results of other players.

Let’s look at this: one player loses 48% of the times, two specific players lose 31%, three players lose 22%, and all four players lose 16.77% of the times. Notice that the chance of each additional player having the same result looked at as percentage of the previous result steadily increases.
(To be more exact we may want to exclude natural blackjacks that have minimal or no correlations to the results of the last number representing all previous players lose.) The correlation would never reach 100%, even if we play with unlimited numbers of players at the table because there is always a chance that one of them gets a bj.

There are three components for BR2 having second low:
When Player A loses, Player B has 65% correlation of losing (excluding bj); When Players A and B lose then Player C has 71% correlation of losing; Players A, B, and C lose then the fourth player (D) correlation goes to 76%.
From the growth of the correlations we can deduct that next one should be around 80%. This would be a base for concluding that all five players lose about 13.4% of the times. If the next correlation were 83% then all six players would lose about 11,1%.
We get about extra 13,4% advancement when all players lose.
Once again, it can be checked from Bluelight’s table that with three players having W-L-L the fourth player L(osing) correlation is about 55% and will be even higher for the fifth (we are only interested with cases when BR2 loses). W-L-L-L occurs 12% of the times, so, BR2 lose and W-L-L-L with 60% correlation adds about 7.2% to BR2 chances.
With three players having P-L-L the fourth player L(osing) correlation is about 68% and occurs 8.8% of the times, and will be even higher for BR2 losing, too. BR2 lose and P-L-L-L with correlation of about 75% adds about 6.6% to BR2 chances.

BR2 modifying basic strategy, when given to have second low, total additional chances should be between 27% and 30%.

I hope it explains why I wrote 3 years ago (even before bluelight’s tables were posted) that if BR2 is given chance to have second high and second/third low gives him about 25% of additional chances to advance when he losses.

Simulations are great and serve as an invaluable tool to check and confirm or question answers and models of any particular situation we encounter in blackjack tournaments. But since there is always a chance of inputting assumptions and set ups differently than intended, and since they can not be used at bj table during the play –developing general understanding of all implications and learning hands correlations is a action not to be missed.

Good cards and fun analyzing plays to all,
S. Yama

 

OK, this is not quite what I simulated.

A new simulation confirms this (all playing basic strategy):
Player 1: BR: 1000 Bet: 925
Player 2: BR: 1025 Bet: 925 (as suggested)
Player 3: BR: 925 Bet: 925 (as suggested)
Player 4: BR: 950 Bet: 925 (match player 3, as suggested)
Player 5: BR: 875 Bet: 750 (takes player 2 low)
Player 6: BR: 900 Bet: 900 (the "one more player who goes all in")

Player 1 finishes: 1: 17.46% 2: 26.63% 3: 22.53% 4: 17.11% 5: 11.54% 6: 4.73%
Player 1 finishes 3rd or better 66.62% of the time which is an improvement of 16.95% over betting 1000 (49.67%).

Simulated result is also close here (BR2 playing optimal strategy, others playing basic strategy):
Player 1: BR: 1000 Bet: 925
Player 2: BR: 1025 Bet: 925 (as suggested)
Player 3: BR: 925 Bet: 925 (as suggested)
Player 4: BR: 950 Bet: 925 (match player 3, as suggested)
Player 5: BR: 875 Bet: 850 (give up 2nd low)
Player 6: BR: 900 Bet: 850 (match player 5, give up 2nd low)

Player 1 finishes: 1: 17.65% 2: 38.98% 3: 19.30% 4: 12.61% 5: 8.31% 6: 3.16%
Player 1 finishes 3rd or better 75.92% of the time, which is a 26.28% improvement over betting 1000 (49.67%)

I couldn't agree more!