"If you’re wondering how big a difference it makes, let’s look at a few examples: Doubling 12v6 gives you a 40.7% chance, compared to 18.6% by standing. Doubling 15v6 gives you a 31.0% chance, compared to 18.6% by standing. Doubling 17v7 gives you a 25.3% chance, compared to 23.7% by standing. Remember, these are percentages of winning two bets in this hand and the next. So, if you’re in this spot, be aggressive and double your chances." With such a lousy hand, should he wait for the final hand and split or DD any two cards? In the second to last sentence of this paragraph, Ken writes ...."and the next." Does that mean these percentages are the chances of winning two bets in this penultimate hand and winning two bets in the last hand? That's a total of four bets. This clarification is distracting me because it appears the situation calls for winning a total of three max bets, maybe four. Not definitely four. Is there an assumption that the player needs to catch up with a two-bet win and then he'll need two bets to win the tournament? If he only needs to win three bets, he could wait for the final hand and hope for a better double down hand or even a hand to split. He would be hoping to win one bet on the 2nd to last hand and then win two bets on the last. Is it better to DD any two cards on the second to last hand? If you lose, and if you have enough chips, you can hope to split and DD enough to catch up on the last hand. If not locked out, you could take the low on the last hand had you lost the second to last. There are a lot of scenarios and I'm trying to understand when to apply these percentages better. Thank you.
I'm a little unclear about some of your question, but I'll start by clarifying the precise scenario that article is about. I can see how the wording could sometimes be interpreted in more than one way, but the intention was to create a scenario where you have two hands left to play, and you need to win a total of two max bets during those two hands. If the max bet is $1000, the percentages given are the chance that you will end the round with $2000 more than you have now, by succeeding in one of the four ways mentioned. The article also mentions several shortcuts I used to derive the numbers. I'm sure gronbog could now give you much better actual numbers by eliminating some of my shortcuts. But I remember this was an eye-opening exercise for me and I had been playing hand 1 too timidly. If I've misunderstood your question, let me know. Otherwise I hope this lends some clarity.
First, I failed to reread the entire article. You wrote, paraphrased "for the technically inclined", and I don't consider myself to be technically qualified. At first, I was happy to get the gist. Then I felt distracted and realized I wasn't understanding something (a couple things as it turns out) and wrote my poorly worded question. That doesn't mean I don't want to read and familiarize myself with the technical information - I'm just not a programmer or mathematician. I simply became distracted by a few details and couldn't just be satisfied with the main point. I'm a bit OCD perhaps, but I'm sick of bubbling. I reread and studied the article for additional clarity. The first way you note to accomplish winning two bets states that the second/last hand doesn't matter. This bothered me because you'll have to make a min bet and could lose, so I think it does matter if your example is that two bets are needed. Perhaps two max bets less a min-bet loss would be enough to win the table but I wasn't clear on that. Also, there's no mention of another player so, I have to realize that the point is simply that these are the odds of winning a double down if you can make two consecutive attempts at doing so, and assuming the first attempt is a push at worst. Examples two and four do recognize that you'd have to push one of the hands to accomplish a two max bet improvement. Your first possibility would also have to include a push, but on hand two/the final hand, so the wording that it doesn't matter threw me off. You do emphasize that this is more prevalent in accumulation scenarios, so when you say "advance", I have to realize that doesn't necessarily mean "win". I play elimination and was thinking this would somehow be a win/lock. Your article's point is that if you need to improve your current situation, whether it's to lock fourth, third, second, advance, win the final table or to just give yourself a chance to hold your ground or survive to the next hand or advance etc..., you're percentages show us the best way to accomplish this. The reader can plug these in to whatever examples they'd like to study or consider. By giving the somewhat specific example of "needing" a double win, I was confused. I was assuming if you can win a double your competitor could as well. So, how does this guarantee advancing as you note. In fact, it does not. But it's your only chance and this shows what to do. I get it now. You state "Remember, these are percentages of winning two bets in this hand and the next." You clarify this with "The key to making the decision to double or not is to examine the total probability of lines 1 & 2 compared to the total probability of lines 3 & 4." So, by stating "winning two bets in this hand and the next", you don't mean four bets total or winning two bets in each of the two hands, and your clarification shows that winning one plus one is inferior. You mean winning a total of two max bets in two hands. Furthermore, you're percentages apply to betting two consecutive hands and doubling the first, win-push or push-win, compared to betting two consecutive hands but not doubling the first one, win-push or push-win. "What we have here, is a failure to communicate." LOL. Great movie. And it's the reader who is failing the comprehension part of said communication. Thank you for indulging my confusion/lack of initial study.
No, I'll take most of the blame here. It's so easy to make statements that can be ambiguous in meaning, and I certainly did it more than once in that article. Also as you noted, if you're playing an elimination-style round and chasing the leader, he or she can also win a double and foil your chances. Non-elimination or accumulation rounds when you have a certain target score are much more likely to provide a scenario where winning two max bets would virtually guarantee that you advance. Anyway, thank for exercising my brain a little after a few years of no tournament action, and good luck out there.
