Posted 09 March 2005 - 08:48 PM
Alright, lets weigh the factors:1. Future Fold equity: He doesn't want to double you up. You can push in every SB and pray he doesn't wake up to a beast, since he fears relinquishing control of the match. This advocates a fold, since you can chop back if you take his statements at face value. Next round, he will have to call 4800 to win 7200 however, and be getting 1.5-1 on such a call. You're inching towards the zone where pot odds allow him to call with any 2 vs. your nearly-random hand. You've lost fold equity if you do not push next hand. This may swing this category to gambling; it depends on Antonio's odds decisions and also how often he'll attack you from his SB.2. Match control: You need over 10xBB to play past the preflop betting round. Assuming as part of this that I'm Danny, I want to be playing deeper stack poker ASAP as I figure my edge expands on each round of betting. This adds value to moving sooner rather than later. A double up now gives you more options later and more edges to exploit. Waiting will still leave you in danger even on a double-up and still playing purely preflop move-in poker. There's a reason Antonio doesn't want to double you up, because you have an edge with every extra betting round before someone's all-in. This favors gambling. Also favoring gambling (should you win) is the message sent by calling an all-in given his aversion to doubling you up. He will be selective in his bullying and may fold his SB to you on occasions due to the daring call you may make.3. Your current hand: You have 78s. You will be behind most hands, but you are compensated slightly by suitedness and connectivity. This amounts to extra outs for this hand. 7's and 8's are likely to be live, as well. Just because you don't play this postflop doesn't negate the fact that your win % is noticably bumped by those extra drawing possibilites. This affects the next decision. 4. Pot odds: There's 8400 to win if you call with your case 6000 chips. You are getting 1.4 to 1 odds. You can take those odds vs. a random hand at +chip EV, but if he only plays A8+, K9+, QT+, JT+ and any pair 77+, you are just getting 1.4 to 1, about break even on chip EV. Other factors affect Cash (tournament) EV. Furthermore, you MUST push next hand, making it a matchup of 2 truly random hands, or a genuine coinflip. There you will be laying 1.5-1 between 2 random and unknown hands, which is -Chip EV as it's even money.5. Future Edges preflop: As your stack dwindles, you will get larger preflop chip EVs on your all-ins but less +Tournament EV due to remaining in the danger zone. With no read on his hands because you will be pushing first or calling all-in vs. a sizable range of hands, when you are in an all-in situation you cannot expect to be a sizable favorite. You will be pushing random hands and the calling range I put him on is a 63% fave over a random hand. This also favors gambling.Bonus decision tool (EV's are overall total expected chip count, not the actual EV of a wager considering the presence of blinds or amount your action is risking; for simplicity):Folding, pushing next hand blind, antonio calls with anything blind:50% chance of ending with 10 BB, 50% chance of ending with zeroEV: 5xBB, 50% survival, 50% Under 10xBBFold, push next hand blind, Antonio calls with above range:8% chance of ending with 10 BB15% chance of ending with 0 BB77% chance of ending with 6.5 BBEV: 5.85 BB, 85% survival, 92% Under 10xBBCall Here, assuming he pushed with his calling range: 37% chance of ending with 12xBB63% chance of ending with zeroEV: 4.44 BB, 37% survival, 63% under 10xBBCall here, assuming he pushed a random hand:48% chance of ending with 12xBB52% chance of ending with zeroEV: 5.76 BB, 48% survival, 52% under 10xBBI'm playing to get to deep stacks. Calling now gives me a 37% chance to cross the 10xBB mark. If Antonio plays as he states, I escape preflop all-in poker only 8% of the time. Due to the source and nature of my edge in the overall match, it is this "escape the move-in" game factor I want to maximize due to the correlation of type of play to my tournament EV as opposed to just the stacks. I'm not fully 2x more likely to win with 3xBB as opposed to 6xBB, but I'm more than 2x as likely to win with 18xBB as opposed to 9xBB. It's this discontinuity in tournament equity and superior postflop play that leads me to gamble. I want to double up when one is offered, not entirely too unlikely, and can still save my tournament and open up my other edges.Then again, this is Sklansky-type evaluation of tourney situations, and Danny had said that's a less correct mathematical model for evaluating this (as opposed to the tools Danny and Gus utilize for examining tourney decisions). But based on it I'm calling, and I eagerly await his quiz answers and reasoning.