Here is an interesting situation which came up at the Fallsview. This will be a multi-part teaser. Here's the initial situation: Final hand Two advance Minimum 25, Maximum 500 BR2: bankroll 2250, bet 25 Gronbog: bankroll 2112.50, bet 500 BR5: bankroll 1650, bet 500 BR4: bankroll 1750, bet 500 BR1: bankroll 2800, bet 500 Let's warm up with a very easy question: What would have been a better bet for me? This one is not so obvious: Was there a better bet for BR2?
It's been a long time since I played in a tournament or tackled a teaser, and looking at this makes me realise that I've forgotten a lot of the rules of thumb I used to have at my disposal. That being said, without hitting the text books to refresh my memory - 350 for Gronbog will cover a lose/push against BR4 (and BR5). And I can't see any reason to bet less than that. [Although, equally I can't see any material benefit over Grongbog's actual bet of 500, since, in either case, BR1 and BR2 will advance if the bet is lost.] As for BR2 - I would have bet 500, but I may well be overlooking something(s). BR1's bet of 500 seems to be the biggest blunder on display, as a bet of 25 would have given a lock.
I was also thinking that I should have bet 350. As Colin points out, it does not expose me to a 1/2 swing from BR4 and BR5, but it does allow me to react to their potential doubles. It also allows me to pass BR2 with a win. However, Colin's second point about a loss being irrelevant is also a good one. I feel better now. As for BR2, I think it depends on his assessment of BR4 and BR5. I think he can assume that they will both bet 500. It's then a case of whether he believes that they will double/split aggressively. If he thinks that they will, he should also bet big. I would suggest 450 minus one chip. He can double for an advancing position if necessary but is not exposed to 1/2 swings by BR4 and BR5. If he thinks that they are basic strategy players, then his bet of 25 is ok, since it preserves the low against everyone and probably locks out BR5.
Even with a bet of 500, he is only exposed to a 1/2 swing by BR4, and it would leave them tied. Similarly, he can tie against a BR4 double without doubling himself. I suppose a lot depends on how ties are resolved, but instinctively I find myself drawn to the 500 bet, to enhance the prospects of the option of not preemptively doubling (if that makes any sense.).
I would be interested in the thought processes used by The_Professional and Dakota for arriving at their bets. However, I actually didn't start this thread to discuss the betting. I only realized that there may have been options in that regard as I was posting. The "Rock and a Hard Place" situation arose after the cards were dealt: BR2: bankroll 2250, bet 25, I don't recall his cards, but because if is bet his cards were irrelevant (to me) Gronbog: bankroll 2112.50, bet 500, hard 16 BR5: bankroll 1650, bet 500, hard 17 BR4: bankroll 1750, bet 500, soft 13 BR1: bankroll 2800, bet 500, soft 15 Dealer: T What should I do and why?
I chose 150 because you would have more unbet chips than BR4 and 5, and if you win you will surpass BR2 and maximum bet for BR5, now I actually think 175 bet, suggested by Dakota, is actually better because it takes into account BR4 max bet. Now to your new question. I think you must win the hand. The difference in win rate between standing and hitting is minimal and it is very likely BR4 is going to double. So, you have to double for at least 150.
You hit it on the head when you said "it is very likely BR4 is going to double". There is a large and very ugly monster lurking there. If I stand and BR4 doubles, then I am immediately locked out. That's the rock. The hard place is that I have 16. So I have to take a card and, in order to cover BR4's double, I need to also double. Since losing the hand will eliminate me regardless of how much I bet, I may as well double for at least 200 so as to give me a few more percentage points on a possible 1/2 swing vs BR1. A double for the full amount would automatically cover all upside possibilities without having to do any arithmetic. The rule of thumb here: Never stand stiff if your opponent can beat you with a double and can double without busting, or even a high probability of not busting.
I like Gronbog's bet of 500 here. After BR2's tiny opening bet, Gronbog cannot win this table without winning his hand. Covering pushes by BR4 and BR5 is irrelevant. The only reason Gronbog would consider betting less than 500 here would be to account for the possibility of getting more than four bets on the table with splits and doubles. The gains from such a consideration are so infinitesimal that it's a bad habit to try and think about it at the table because Gronbog might miss something bigger. 500 is the best bet. BR2 has conflicting needs here. This is not surprising, as he is BR2 and first to act in a two-advance table. Need #1: Preventing Gronbog from cutting under him by taking the low. To prevent this he would bet no more than 135. A bet of no more than 95 covers a loss-push against Gronbog and a full swing against BR5 as well. Need #2: Covering the double downs by BR4 and BR5. He can bet at least 405 to cover BR5 with a single bet. A bet of 495 covers Gronbog's double down while also covering a push by BR4 in the event the bet is lost. Of course, covering a push by BR4 doesn't help BR2's cause if Gronbog takes the low. Need #3: Threaten BR1. BR1 is ahead of BR2 by more than a max bet. But were BR2 to bet 495, BR1 must bet at least 445 to cover BR2's double down with a single bet, exposing him to full swings by both BR2 and Gronbog. A small bet by BR2 virtually hands BR1 a lock if BR1 sees the opportunity and bets 5. Avoiding handing someone a lock is almost as important as locking someone out, which should be your first consideration when choosing a bet size. Need #4: Force Gronbog to make compromises. If BR2 bets high enough, Gronbog can take the low and get at least a 50% chance of finishing higher than BR2. However, Gronbog has to consider covering double downs by BR4 and BR5. Gronbog also should consider threatening BR1. If BR2 bets 440, he covers Gronbog's double down. A bet of 440 by BR2 forces Gronbog to bet only 325 to take the low on BR2. This bet by Gronbog of only 325 gives BR1 the opportunity to bet 5 and lock himself a spot. Holy cow! That's a lot for BR2 to think about! It would take a real animal to think about all those details at the table... I think a bet of 440 is best for BR2. He is hoping for mistakes by Gronbog (unlikely) and BR1, and asking Lady Luck for some assistance.
Because of BR2's tiny bet, Gronbog must win his hand to win this table. That's already a tall order, and it's been made much harder by these stinky cards. The safest bet in the whole casino right now is that BR4 will double down for 500 if Gronbog stands on his stiff 16. Even a dull opponent would know to do that. And Gronbog is right; he will be locked out if he stands on this 16. Since Gronbog has to win his hand and since he absolutely cannot stand on his hard 16, he may as well double for 500 and hope for a miracle.
