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This will be pretty messy if I don't define some variables, so here goes: P$ = Current size of the pot S$ = Minimum of your stack vs your opponent's stack F% = Chance of your opponent folding to your shove (this should be between 0 and 1; divide percentages by 100 to get corresponding value) W% = Chance of you winning when called (this should be between 0 ...

The decision is based on the extra equity you gain in the tournament if you win. In the first instance, you have an 80% chance at a 600bb stack, and a 20% chance at not cashing. Your ROI with a 600bb stack would need to go up based on that stack to make the call worthwhile. The breakeven point is .8 * 300% * advantage + .2 * 300% * 0 = 300% The left side ...

There are thumb rules for the preflop equity (against a single random opponent) of pocket pairs and suited-connected combos. For the equity of a pocket pair, you calculate how many cards away from 2 your cards are (for example, Queens are 10 cards away from 2), multiply by 3 and add 50%. So QQ's preflop equity is approximately: (10 * 3) + 50 = 80% For ...

If you know your post-flop equity, your cards are irrelevant to the calculation here. That said, we have one crucial bit of information that is lacking: what range of hands is your opponent reraising with preflop? If he reraises with 100% of his cards and then folds everything but AA/KK, then it's pretty easy to make this profitable. If he only ever ...

I don't think anything is proven, not even that ev_sb >= 0, so the only bounds we have are trivial: -0.5 <= ev_sb <= 1. An easier question is "What ev_sb do people find solving abstracted versions of HUNLHE". It would be be interesting to know the sorts of values people are getting, i.e. 1) The value of the (abstract) game from the SB's ...

The EV is (% he folds to All in * Current pot size) + (% of times opponent calls * % you will win * Total size of pot) - (% of times opponent calls * % you will lose * Amount that you bet/shove). On the left of the "+" sign are the times without a showdown. On the right are the times with a showdown. The times you win or lose can be calculated either ...

You can get some tighter bounds by calculating the expected value of some specific strategy (call it S1), knowing that the GTO strategy will be >= S1. For instance let S1 be the strategy where the small blind goes all-in with AA, and folds all other hands. It is a pretty simple probability problem to calculate the expected values in that situation. There is ...

I think there is a problem with your definition of ev_sb; you've included a recursive definition that doesn't make sense to me. Also, your definition of r_ev has possibly complicated the problem definition. Instead of r_ev is the part of the initial pot of 1.5BB the sb wins when r I redefine r_ev to be the EV to the SB when SB open-limps or ...