I made a careless error on the final hand of the preliminary round at https://www.blackjacktournaments.com/tournaments/mini-baccarat-tournament.2577/ yesterday. I thought I would mention it so that you don't make the same mistake. This was a 2 advance table with a secret bet on the final hand. Limits were 50-2500 for banker/player and 10-500 for tie. A winning tie bet pays 8 to 1. Note that a winning tie bet can do some serious damage here, being worth 4000 for a max bet. Also, it didn't enter into it here, but 5% commission is charged on winning banker bets. Betting order doesn't matter here, since it was a secret bet. Bankrolls were as follows: BR1: 5600 Me: 4561 BR3: 4190 BR4: 1750 BR3 is right on my tail and BR4 is in trouble, but not out of it, because of the large maximum on the tie bet and the small possibility of swinging the rest of us. I had brushed up on Wong's tournament baccarat chapter the night before and remembered his advice for this situation: when on the bubble with a secret bet and with one or more contenders, play his 'Max-Bank' strategy. This strategy says to bet the max on bank and also the 'max' on tie. The logic is that your opponent(s) must first be lucky enough to bet opposite to you (secret bet) and also lucky enough to win their bet in order to catch you. As well, if the hand is a tie, the banker/player bets all push and you maintain your lead with your tie bet. This all assumes that your opponent(s) will bet big which, as far as I have observed is almost always the case. The odds of you maintaining your lead are quite good. More than 75% for one contender. So I bet 2500 on banker, 500 on tie. Can you spot my error? There is a small hint in my description of Wong's Max-Bank strategy above. Bonus points if you do not consult Wong's book in order to figure it out.

If BR3 also bets max on bank, your 500 tie bet will give BR3 a net 500 gain for both the player-win and the banker-win outcomes. So BR3 would then overhaul you unless there is a tie. I think a bet of 150 on the tie would be enough, covering the possibility of BR4 winning 4000 by just betting max on the tie, and also giving the possibility of overtaking BR1 if BR1 doesn't make a tie bet. And it means you might still stay ahead of BR3, even if they bet a little less than 2500 on banker.

Nicely analyzed, as usual, Colin -- and am I to award you the bonus points? I wrote 'max' in quotes when describing Wong's strategy because what he means by 'max' in that case is to bet as much as you can without compromising your banker bet. In this case, by betting more than 370 on the tie, my banker bet became useless vs BR3, unless he also bets a sufficient amount on tie. As it happens, I was forgiven by the baccarat gods as the bets came up as follows: BR1: BR 5600, Bets: 2500 Banker, 0 tie Me: BR 4561, Bets: 2500 Banker, 500 tie BR3: BR 4190, Bets: 2500 Banker, 200 tie BR4: BR 1750, Bets 1750 Banker, 0 tie (???) It was fortunate for me that BR3 bet 200 on tie, so I had a lock, once the bets were revealed. At the time, I only realized my error when the chips were counted and I saw that I had only prevailed by a margin of 71. Looking at it now, BR3's tie bet of 200 could have been reasonably predicted, since it covers a max bet on tie by BR4 and beats any other player who might not have bet on tie. So I was actually lucky that the situation called for a 200 bet on tie by BR3 and that he was smart enough to realize it!

Yes, please. I actually still haven't looked at what Wong has to say. I've been trying to think through some of the issues from first principles, wondering whether there is anything to be said for skipping the tie bet altogether, and just betting enough on player or banker to cover a max-bet (player) win by the nearest challenger. I suppose it comes down to how sure you can be that the opponent will place a max bet, and whether there is any realistic prospect of them betting less than max but still big, so that we have the possibility of keeping the high and low when a max bet from us would give up the low. I think BR3's best move might have been to place just the tie bet. BR4 is then locked out, whatever happens, and there is a good chance of having the low against BR2 and/or BR1 (as the actual bets show would have been the case). In fact if BR1 and BR2 place big bets, one on player and the other on banker, BR3 could even get a lock to advance.

Just a nit, not significant in this case, but potentially so in other situations -- one cannot generally bet soley on tie. One must usually place a banker or player bet on each hand. However, if the tie bet wins, the banker/player bets push, making this irrelevant if one is relying solely on the tie for success. As someone who started out playing blackjack tournaments, it took me a while to realize that going for the low generally has very little value on the final hand in baccarat tournaments, for at least two reasons: Contrary to blackjack, where the most likely outcome is that your opponent will lose their hand, the most likely outcome in baccarat is a banker win. The odds of a player win are not far behind. On the final hand when ahead, going high on one of these two bets are your best two choices for success. On the final hand and trailing, if you're considering going low vs an opponent, you're counting on him to lose, which means that the other side must win. In that case, why not put your chips to work on that other side? These are the reasons why, on the final hand, if your position is is jeopardy (read the chapter for the definition), Wong always recommends a Max bet on banker or player. On the final hand, once you have made your banker/player bet, if you can make a bet on the tie without compromising that bet, then there is absolutely nothing to lose by doing so. One should bet as much as possible. This is what Wong refers to as making a 'max' bet on tie. Now, of course there are exceptions, and it would be useful to discuss any that people can think of. (edit: the opening statement of the next paragraph and the conclusions drawn from it are incorrect. See subsequent posts for more discussion on this point ) In BR3's situation above, he does not need to bet small in order to gain a lock when BR1 and BR2 bet in opposition. He is guaranteed to swing one of them in that case. The only situation I can see in which a small banker/player bet would be superior to a large bet for BR3 would be if BR1 and BR2 both bet big, both bet on the same side and both lose. Then it would not matter which side BR3 bet on. On the other hand, the same small bet would be less effective if one (or both!) of BR1 and BR2 bet small, since a swing on the wrong one would then be useless. I guess it depends on your read, however, as in blackjack tournaments, the rule of thumb, when in doubt is probably "when in doubt, push it out". Note that all this max-bet-on-the-final-hand stuff is for when the bets are secret. Of course, if you could see your opponents' bets then you would correlate and oppose them in the proper amounts as appropriate.

I hope you are enjoying and appreciate playing bac tourneys the more you play them. I would rather play one bac than two bj tourneys for fun of it and one instead of three for the value coming from the skillful plays. The situation you described is quite complicated (more than usually). Perfect plays require figuring your bets based on assumed opponents’ bets. Weighin the ranges of their (secret) bets have to be based on “real” reads you get from the pattern of the previous plays and observed personalities. The ranges are often defined by the bets limits and differences between the bankrolls. Complications arrive from the bulk of data. For example, if you attribute percentage chances for two chosen bets for the main bet and Tie bet for three opponents you will end up with 64 possible situations. In reality, though, many of them lead to the same conclusion There are at least ten “first rules” for playing strategies, some of them are: Bet Bank if you are in br position and Player if not (playing against average opponents). Assume that opponents make perfect (or worst for you to succeed) bets. Lock out max number of players if possible (becomes less important if you have higher number of opponents to overcome). Consider that experienced bj players (but not bac players) will make incorrect bet of “having low” and will spend no more that their lead over you (this sometimes may be an okay bet but almost never is a perfect bet). The other possible bet made by bj players more often than bac players is a minimum bet. Observe and strongly consider opponents making maximum allowed bets. Make the exact bet. Since in most tourneys you can keep the score card you can write down and calculate a precise bet. The last rule would apply to your play. Since you had 371 lead over BR3, you didn’t have to bet max on Tie. You could go 4000 – 371 /8 , but my preferred way of calculating the bet at the table would be: If I underbet by 50 (which pays 400) I still need additional 30 in winnings, so I can underbet max bet by 40, thus the bet is 460. Can you imagine the frustration if BR3 had bet max Bank and 100 Tie? Beating your score by 29 chips. His bet in the range of 50-120 is somewhat reasonable as it gives him more than 371 difference between your bankrolls if you don’t bet the Tie. Analysis of your bet has to include weighin the chances of your opponents’ size and the side bets, attributed to you best but realistic knowledge of their playing behavior. The easiest play (not correcting for the opponents’ patterns) is for BR1. Can you make those bets within couple of minutes using pen and paper? BR4’s bet is somewhat more complicated. He has to assume the chances of BR1 to BR3 making a Tie bet that covers his max Tie bet. Assuming that opponents would bet Tie with 90%, 80%, and 70% makes chances of advancing with a Tie hand l0%, even when the chances are 70-60-50% two or more opponents cover it 65% of the times (times 9.5% chance for a Tie) Slim chances. Not betting the max Tie gives him 1000 chips more if the hand is won and increases the chances of advancing if two of the opponents make mid range bets and lose. All-in, no Tie, on opposite side what is the prevailing opponents’ side would be my bet. Note that about 60% chance of each opponent making Tie bet equals about 15% chance that each of them make a bet that losing it gives BR4 advancement when his score is 3,500 and doesn’t if his score is 2,500. S. Yama

Are you talking about a tournament-specifc rule here? I've never played in a tournament, but certainly all the bacarrat games I have seen in the U.K. allow a lone tie bet. Only if he wins the hand. If he loses it then the BR* who bet the same side he did maintains his lead, and the BR* who bet the other side increases his lead. But by betting small enough to take the low against both, one of the two is bound to fall behind.

Yes, this is a tournament thing. All the baccarat events I have participated in have required a participant to make either a player or a banker bet on every hand.

Yes, good catch. I don't know what I was thinking. With secret bets in play and a high probability of large bets by BR1 and BR2, perhaps this is one of those cases where going for the low would be better for BR3. Given the fixed probabilities of each outcome in baccarat, it would probably not be too hard to get the actual probabilities using a spreadsheet.

I am enjoying playing them and learning as I go. I can also see great potential for value in them. Even with my limited amount of experience, I have found the level of skill at my local events to be low and have found that even the basic advice in Wong's book has served me well. Having played in a few, starting to get a feel for it and now, discussing things here, I know that there is a lot to learn beyond what Wong has to say and that can only lead to more opportunity. I always appreciate your insight and would be interested in your analysis of BR3's situation. Specifically, what do you think of the possibility that a low player/banker bet might be a good choice for BR3?

BR3, okay, again, rarely you will have no clues as to the side and size of opponents’ bets, which makes a big difference. If you saw a player making Tie bets a few times and Tie bet may effect the last hand you can be almost sure s/he will make it on the secret bet. Once, in S. Cal where they had bac tourney for the first time (mostly Pai Gow players, who never played bac before) on the last hand in the final there was only one Tie bet out of 10 players, though the bankrolls were close – and that was predictable, as nobody ever made that bet during the round. It is worth noting that in bac, other than advancing by winning your bet, either big enough to overcome opponents or other player losing, you have a considerable chance of advancing when you lose but opponents with higher bankrolls overbet and lose more than you needed to gain to them. As BR3 at the table I could have go like this: The first thing I would notice is that to lock out BR4 even if I lose, I can spend no more than 680 (he can double his brl of 1,750 and I have 4,190) gap to BR1 1,401 (necessary min Tie bet 180) gap to BR2 371 (necessary min Tie bet 50) lead over BR4 2,440 (necessary Tie bet to cover his max -200) My quickest base bet would be 200 Tie and 350 (+200 to cover the lost Tie bet) main bet opposite of what I think BR2 may bet (and/or BR1 combined, if I think he makes a big bet) –total 750. (Note that I don’t have to bet more than the gap, as BR2 has to lose at least the minimum bet when I need swing). This bet would cost 70 more than I could afford. Adjustments needed and follow: Because of small probability of BR2 betting very low, and slightly better chance of one of the two not making Tie bet, I have to lower my main bet and keep the Tie bet. Also, I would like to make correction to beat BR1 and BR2 if they use similar goal strategy. They may round up their bets to 50s’ or 100s’trying to achieve the same coverage. The only possible strategy for them using low bets I can notice is that they may make a “mistake” of keeping more unbet chips than my bankroll of 4,190 and keep 4,200. This mean my main bet has to be slightly bigger than the Tie bet to end up over 4,200 if won. I have 680 “to spare”, not much to gain by winning my already small bet, and not enough to cover BR2 betting minimum [for unknown reason, or bj bet] and winning, so I would bet the Tie for 250-275 and main bet 275-300. It covers BR1’s and BR2’s Tie bets if they round up to 25 their Tie bets to beat BR4’s max Tie bet, and covers by 100+ if they keep more than my bankroll, and lose while I win my main bet. That would be my bet if I had no time to consider other options and players were somewhat experienced, with no information on their characteristics as tournament players. Just to see some numbers, let’s assume that the total bet by both BR1 (and respectively BR2) is >=2,100 (1,000) 60%, 1,400 to 2,100 (>250) 30%, and <1,400 (<250) 10%, and you have only 50/50 info on what side they bet, and there is 70% chance they each make Tie bet, but half the time it is the calculated Tie to just beat BR4 max Tie bet. Such situation would advance the above-described bet 67% of the times. However, it grows quickly if the chance of them betting opposite of each other, and/or you knowing better than 50% the side of bets either one of them makes. Next to consider is betting max, or near max, with or without Tie bet. The ranges are too big to cover them all, so I would have to have a description of at least some of your educated, estimated guesses of their possible bets. S. Yama

I have only played at this particular event 3 times, however I have observed that the players will bet max on banker/player almost 100% of the time on the final hand, secret bet. This is regardless of whether they are ahead or behind. Tie bets are less common and could be characterized as similar to what they would bet during the rest of the round.

I am not sure how to structure a helpful post, not because the subject is super complicated, but because it is multi-elements conditional, and includes calculating uncertainty. We have to assume probability of player’s side bet, its size, and combine it for multiple numbers of players. When we say that we have no idea what side somebody is going to bet, in case of baccarat (where there are only two options) we mean that the chances are 50/50. When we think that an opponent is somewhat more likely to bet, lets say, on Bank we can assign 60% Bank and 40% Player, etc., etc. It is never 100%, but can be close to (as gronbog said), unless we inadvertently see the secret bet, or it is made in open. It takes a lot of experience to assign meaningful probabilities, but it can be done, and should be practiced all the time. It can be done throughout any tournament on any action we witness; The difficulty is to either make scrupulous notes, or be able to mentally confirm our guesses to real outcomes of particular groups of guessing and gradually improve our assessments. This also applies to other games like poker and bj tournaments. For example, if you are sure that two out of three times (the exact number depends on the rules and brls), when on the last hand you bet first and have a lead and make a big bet your opponent will match your bet – it is the preferable play compared to taking low. This particular weighing the odds that can be utilized happens rarely but when it does it’s so sweet (on a personal note, it helped me once to advance to a big Riviera final [about 20 years ago, lol] when a good player on third-to-last hand had multiple split/doubles, and his bet on the next-to-last hand showed me, that mistakenly he thought that he had a lead). Back to baccarat, and BR3 situation when two advance. Let’s omit the Tie bet and its consequences and treat chances of Bank and Player as equal for the clarity of the picture. If you are certain that both BR1 and BR2 bet more than their lead plus your “small” bet, and you have no indication on what side they going to bet you have exactly 75% chance that at least one of them will lose. Your chances get smaller the more likely it is that they bet on the same side. All the way down to 50% when they both (100%) bet the same side. Your chances of advancing grow bigger the more likely it is that they bet on opposed sides. All the way up to 100% advancement if one bets Bank and the other bets Player. It is possibly counter intuitive to some, but even if you are 100% sure that one of your opponents bets on one specific side and you have no clues to what the other player may bet, your chances are still, right in the middle at 75%. There is a beautiful symmetry to the distribution of your chances based on the sides they bet on. If one player bets 100% one side then for every 10% increase/decrease chances from 50% for the other opponent your chances change 5% from the middle of 75%. (So, 100% Bank and 60% Bank your chances are 70%, and for 100% Bank and 40% Bank it is 80% chance, etc.) Since it is rare to be so certain of your opponents bets, lets note that for every 10% difference from the 50% chance of picking particular side for both of them, the numbers change by 1, 3, 5, 7, 9% compared to the last one. This makes it going up or down from 75% by 1%, 4%, 9%, 16%, and 25%! See the pattern? That sequence is squares of 1 to 5 [(1sq.=1, 2sq.=4, 3sq.=9, 4sq.=16, ...) Rule: xn=n sq. So, for players betting 60% Bank, 60%Bank it is 74%, 70%B and 70%B it is 71%, 80%B and 80%B it is 66%, etc. and for 60%B and 40%B it is 76%, 70B and 30%B it is 79%, 80%B and 20%B it is 84% chance of advancing.] BR3 has to consider at least 3 bet sizes for each of his opponents. 1. Op.’s medium bet - we need to win our small-medium bet to overcome the opponent when he loses 2. Op.’s high bet – we can afford to lose out bet 3. Op’s small bet – we can be lock out even if we win and the opponent loses Since the chances of advancing by one of the opponents’ big bet loss, it is most likely the best play if we assume high probability of their big bets. The chances of advancing with max bet (or even a medium bet that allows BR4 to overcome us if he wins and we lose) would be a really poor choice, as we advance almost exclusively when we win and one of the other BRs loses, which could be the half of chances compared to taking “low” if opponents bet big. For the particular situation the danger of the “low” is being locked out if the opponents bet small. Even if one of them bets small 100%, the chances of low are the same as for high because you advance if you win versus you advance when big bettor loses. If you assume that each of your opponents makes a bet that locks you out more than 53% of the times then making a big bet becomes more valuable (at about 39% each). S. Yama PS Of course had to mistype something, the breakeven point for two opponents making big bets or very small ones is 57%.