In Stanford Wong's book, "Casino Tourament Strategy," it states that on the last hand if you have the 2nd highest chips (BR2) you should bet at least double the amount you are behind BR1 plus a chip.... My question is: what is the mathematical reasoning behind this? Could someone further explain? It's a great book but doesn't mathetmatically explain the exact reasoning of what I bolded above. Would be great if someone here can break it down for me. Thanks!
This is the first step of the “Rule of 2, 4 & 5” that I have written about. An example will illustrate the value of 2x plus a chip: You trail by $100 so you bet $205. the leader then bets as much as he can without giving up the low. He bets $300. If you double for another $205, you will have the high by $10 over his single bet win. It is the “2x plus a chip” that guarantees that possibility. There are additional benefits by betting 4x (beat a blackjack with a double), or 5x (beat a single win with your blackjack). Others here have pointed out benefits of 3x as well.
Thanks for your explanation, Ken, but what's to stop him from doubling his $300 and beating you, too? So IF we were faced with the dillema of being BR2 on last hand then this is truly our best strategy, eh? Can you show an example of the betting 4x or 5x? Yes, I read about your rule of 2, 4 & 5 somewhere.... do you have a link where you discussed those basic tourney strategies? Thank you.
https://www.blackjackinfo.com/blackjack-tournaments/the-rule-of-2-4-and-5/ And I’m editing my message above to correct my descriptions of 4x and 5x. That’s what I get for posting after a long day of visiting sites in Washington D.C. For your other question, if you find a way to protect against the leader winning a double down, you’re going to be unbeatable!
Thanks for the explanation, Ken. So where does betting UP TO half of the bet come from? Say, double your deficit + a chip up to half your balance.... is the latter for doubling purposes only?
There are a number of reasons that Wong may state this. My guess is that he is merely pointing out that unless you can make a full double, the benefit does not exist. If your deficit is more than 1/4 of your total bankroll, these options don’t work as described because you don’t have enough chips to implement them. You really have to hope the leader does not fully protect his lead in that case.
I believe if late surrender is offered, betting more than your deficit gives you the option to LS and possibly get the high. You are behind 100, you bet 205 (If no 2.50 chips are allowed, bet 206 or 210 if reds are the lowest denom.). When BR1 looks to have a loser or actually busts, you can LS if it secures the lead for you. Also, if you can DD, the larger bet gives you the chance to win more. If you need to split and possibly split to 4 hands or 3 hands, the bigger bet may also help. It may give you more chips if you win all hands. It may give you enough to be BR1 should you win a DAS or two DsAS, allowing you to lose one hand. Of course, this works for any bet amount when you need to win one or win two etc... and you bet the correct amount (the bet doesn't have to be 2x+1).
So say our deficit was more than 1/4 of our total bankroll on the last hand and we are BR2. What would then be our best bet if we're on the button?
Bet more than your deficit so that a win by you will pass BR1 if they push. To succeed, you will usually need either a half-swing or a full swing. If BR1 bets poorly, a simple double down might be enough to win. In reality, each specific bankroll scenario is going to have its own peculiarities to examine.
Actually, that's precisely what happened at my final table yesterday. 4 players remained, I was BR2 with 25,500. BR1 had 45,000, BR3 with ~10K and BR4 with 8,000. Secret bet last hand. I bet 15,200, approximately holding back 1-2 chips more then BR3 as I knew I had 2nd place locked up. I didn't wanna bet 20,000 as a win by either BR3 or BR4 and a loss by me puts me in the 3rd-7th same prize spot... of course if I lost my 15K bet and they won I guess the same thing can be said, right? So I'm not 100% sure what my best bet was here. HOWEVER, perhaps a better bet would've been 12,250 so that I could've split if possible? Bec my 15,200 bet would only allow me to double for less but already explained my reasoning for betting 15,200 in this spot (holding back 1-2 more chips then BR3). So, did I do the right thing? Turns out BR1 only bet 500, but since it's secret I couldn't see it but had I seen it I would've most likely taken the high by betting 20,600; wouldn't you?
A few thoughts... You don’t have 2nd locked up unless you bet less than $500 (assuming bj pays 3:2). Instead, you correctly note that your larger bet opened the door for you possibly finishing in 3rd or 4th place. BR1’s bet is terrible. Why not at least $6100, secret or not? If he bet the $500 in the open, you should definitely take the offered high (assuming there’s a decent difference in the prize money for 1st and 2nd). If I’m in your seat making a secret bet, I’m going to assume that BR1 will take the high away, but I want to bet enough to win with a swing. That is, I assume BR1 has bet more than $6000. If he loses that bet, I need to end up with $39,000 to win first place. So my bet in your spot would be $13,500. Because of the logic above, I would not have wanted to split my bankroll instead, even though betting so much means I can’t split, as you noticed. What do the rest of you guys think? Do you like $13,500 or $20,000 here? I’m starting to like the 20k the more I think about it. I’m not sure what good the extra unbet chips are if I bet the smaller amount. At the table with limited time, I think I would have bet $13,500. But I think $20,000 is actually a better bet. (Edited 7 minutes after I posted, to remove a line of thought that made no sense.)
Well, I had no idea at the time, but BR1 was actually a high-roller player who only played in 1 other tournament before that one he won! From the way he was betting (he made a few big bets after my BJ 2-1 all in that won 20K), I really couldn't tell if he was a noob or expert so couldn't utilize any info on what his last bet secret bet could've been! I also want to note that I made my move on hand 6, bec I had calculated that the button would be right on me on hand 12! A terrible place to be in at the table... had there been a hand 13 I would've been good but chose the ideal time to go all-in given the circumstances even though I would've preferred to wait later ! Anyway that's why he made such a bad bet bec he obv didn't calculate (25,500 x 2) to end up with 51K... but too bad I couldn't see it! BJ in this tourney as I mentioned above actually pays 2-1 ! So if BR3 would've BJ'd he would've ended up with ~30K suddenly, eclipsing me! So it's sorta hard to account for that and tbh I wasn't even thinking about that possibility by either BR3 or BR4 -- I was just calculating the max they could end up (16k, ~20k), if they both won their hands. You are correct that I didn't have 2nd locked up; but rather, I had a good shot at being BR2 given the 4 bankrolls. Now come to think of it.... was betting 15,200 a bad move on my part since it's a secret bet since BR3 really isn't betting before me, and the real reason why I did it was to hold back a little more than him in case dealer beats us all? Turns out I ended up pushing my last hand so would've have mattered what I bet but of course no one knew that before the hand played out..... but I still want to know how good (or bad) my 15,500 bet was though! But I really dont think I should've went all in due to the fact that there were 2 other players with 8K and 10K remaining and being swung in that situation would've seriously sucked since: 1st = $15k 2nd = $5k 3rd to 7th: $1k
$15,500 is a fine bet. It does everything I mentioned in my earlier post advocating $13,500. But let's look at bigger bets... The only additional risk you run by betting $20K instead of $15,500 is the chance that you lose while BR3 or BR4 pushes. You already will be passed by them if you lose and either or both of them win. So almost all of the "swing risk" already exists with a bet of $15,500. For my opinion, I would trade the additional half-swing risk on the downside, in order to gain a half-swing benefit on the upside. In other words, if BR1 pushes (or of course, if he loses), I win the tournament if I win my hand if I bet at least $20K. That offsets the downside risk (equal probability of half-swing down and half-swing up, and I'm risking $4K in prize money to gain $10K). (Parse that idea carefully; there's a lot of data in that sentence.) It's also worth discussing whether more than $20K is a good idea. Not knowing what BR1 bet, I didn't see any point in betting more than $20K. With the benefit of hindsight, we now know that betting a little more does help, because he made a minimum bet. The question of whether it makes sense to essentially go all-in because of the chance BR1 might bet very small is difficult for me to answer. It would partly depend on player personality. Much of my tournament play over the years has been against very skilled opponents, and I still to this day often don't account sufficiently for possible bad decisions by my opponents. Live and learn. Maybe all-in $25,500 isn't such a bad idea here.
I like the bet of 20k. Beating BR1s push for an extra $10k seems like a good trade for exposing yourself to pushes by BR3 and BR4 which give up $4k. I would have also assumed that BR1 would protect his lead and so I would not have seen any value in betting more. I rarely go all in on the final hand of a no limit event. Holding back a few chips has value for the case where everyone else goes all in or holds back 1 or 2 chips.
