3Betting Vs a Static Opponent Given Certain Bubble Factors

In poker, aggression is important, but it's also important not to take things too far since you can never get 100% of the prize pool and you are simply helping your opponents make money if you are always too aggressive. Tournaments have bubble factors that should adjust your decisions as we've shown. We've even shown a strategy for unexploitable opening ranges with 20 and 30 big blinds at different bubble factors and vs different 3bet ranges.

But what about your aggression? What about when someone raises 2.2 BBs and you are trying to decide whether or not to jam? How should bubble factors affect your jam range given certain assumptions about your opponents?

Let's say opponent has a "static" or unchanging strategy. He does not adjust at all to bubble factors, and he is predictable in always open raising when it folds to him with 10% of hands regardless of position. He will call 3bet shoves with 99+,AK,AQs (calls with 42.2% of his range). If these assumptions are correct, how often can we Jam vs this player from the button if both the blinds are on autofold?

First we determine how often opponent calls a shove. This is 4.2232/10 since he calls with  4.22% of hands out of 10% or 42.23%. We then run the math assuming we gain 4.5BBs when he folds, and when called we win 22.25BBs when we're called AND win, and lose 20 when we lose. We then multiply that total expected loss by the bubble factor since chips we stand to lose are not equal to the chips we gain. We can adjust until we find the break even point. Based upon these percentages we can find which hands a shove is break even with or better. The real optimal solution may have some flat calls in there, and thus might shove with more premium hands and a small percentage of bluffs and just call with the remainder, but it's not a huge mistake to ignore these and jam or fold.

Jam with:
Bubble Factor of 0.8 jam such that you are 25.74% to win when called:
22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
Bubble Factor of 1.0 jam such that you are 32.77% to win when called
TT+,AQo+,AJs+,KJs+,QJs
Bubble Factor 1.2 Jam such that you are 38.58% to win when called
TT+,AKo,AKs
Bubble Factor 1.4 Jam such that you are 43.47% to win when called
JJ+,AKs
Bubble Factor 1.6 Jam such that you are 47.64%  to win when called
JJ+

Charted neatly below to eliminate the wording
bubble factor|% to win| hand range:
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+

As our opponent folds more than 57.8% of his hands we can push with a lower percentage to win vs whatever calling range he calls off with.

With a larger number of big blinds like 30, you need to Jam with a tighter range of hands since you are giving your opponent a better payout when he calls, and gaining less proportionally to what you lose when you are called and behind.

Obviously a tight player isn't the ideal target to 3bet, but if you have a decent hand you can certainly go for it.

What about other player types? Although I haven't gone through to do the work to define the exact hands, I have came up with the percentages of a few scenarios.

20BB 3 betting over
% to win needed when called if opponent opens with

35% of hands and only calls with 99+,AQ+,AJs,KQs (calls 13% of the time he opens)
bubble factors
0.8  0% any two
1.0  0% any two
1.2  6.55% any two
1.4  13.99% any two
1.6  20.34% any two

30% of hands and only calls with 88+,AJ+,KQ (calls 20.61% of the time he opens)
bubble factors
0.8  0% any two
1.0  6.32% any two
1.2  14.42% any two
1.4  21.23% any two
1.6  27.04%

opens 25% hands and calls with 88+,AJ+,KQ (calls 24.7% of the time he opens)
bubble factors
0.8  any two
1.0  any two
1.2  22.29% any two
1.4  28.47%
1.6  33.75%

Opens 15% of hands and calls with 55+,AT+,KQ (calls 70% of the time he opens)
0.8 36.88%
1.0 42.86%
1.2 47.80%
1.4 51.95%
1.6 55.50%

Opens 20% and calls with 55+,AJ,KQs (calls with 42.2% of the time he opens)
0.8 25.74%
1.0 32.77%
1.2 38.58%
1.4 43.47%
1.6 47.64%

Opens 10% and calls with 99+,AK,AQs (calls with 42.2% of the time he opens)
Jam with
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+

It's important to notice that opponents SHOULD call off much tighter as bubble factors increase, but if they don't, you'll have to shove much tighter yourself.

Against an opponent who calls off with the SAME range of hands and raises with the SAME range of hands, you are going to have to tighten up dramatically as bubble factor increases both in your opening range, your call off range and your 3bet range.

However, what tends to happen is opponents might try to exploit by opening just as wide near the bubble, but fold more tightly because they are aware of bubble factors or give too much respect to the 3bet believing that an opponent wouldn't 3bet shove without a huge hand. Or they raise without anticipating the possible reraise and then once it comes they start worrying about the money so they tighten up.  So I believe there are certain types of opponents where your range won't change that much, and other types in which it will actually WIDEN because of how they play, but for now until I run the math to prove it, that remains speculation.

What I'm very interested in seeing is if an opponent opens up with say 20% of hands and always assumes a certain 3bet range and actually adjusts his calling off range for the bubble, but not his opening range. Since his calling off range will tigthen up as the bubble factor increases, it becomes correct to raise more, if not for the fact that our bubble factor also increases. There is definitely a point in which WIDENING your 3bet range as you get closer to the bubble is correct to certain opponents, but I will be interested to see how great of an adjustments to call off range opponents have to make for that to be the case.

In the future I hope to work some of those numbers.