what poker players can learn from Blackjack pros

[CORed]

Blackjack pros tend to use sophisticated statistical calculations more than poker players. This is true for a variety of reasons.

They can: In blackjack, your opponent (the house dealer) plays a fixed strategy. You know that the dealer will always hit 16 and stand on 17. This makes it possible to calculate everything out to 6 decimal places. It also means that there is usually no doubt what the correct play is. In poker, things are rarely this cut and dried. Your opponents can and will do whatever the heck they want to.

Blackjack pros have a very small edge relative to standard deviation: Even a high positive count will only give the blackjack player perhaps a 2% edge, and due to the necessity of not being too obvious, blackjack pros are often playing with much lower EV, often negative. This requires a large bankroll, and makes reducing variance critical, if the blackjack pro is to avoid going broke.

[BillC]

Here are some numbers. I calculated the break even point for CE for utility -1/x, (which corresponds to 1/2 Kelly) for various drawing odds.
I then calculated the excess (over the pure EV based required pot size) you would need for 1:n shot, assuming one unit to see the next card. The formula is
Bn/(B-n-1) for the pot size needed to break even on a 1:n shot at cost of 1 unit, with bank B. Subtracting n gives the "CE = offset":

n(n+1)/(B-n-1)

The chart below shows the excess pot size required (to break even in CE) for 1:n shots, n=1,...,30 and for Bankrolls 50, 100, 200, 300 units.

Of course, I ignore implied odds and assume you pay exactly one unit to draw to a winner.
E.g. suppose you are drawing to a 1:22 shot, paying 1 unit to see the one card, and your bankroll is 300 units;
then you need 22 units in the pot to break even in EV. In CE
terms, you need an extra 1.8 units to break even, so you'd need pot odds of 23.8:1.

This is a first attempt to quantify the idea that you should
avoid borderline hi-variance draws if your bankroll is not relatively huge.
-BillC


n/B 50.0 100.0 200.0 300.0 600.0
1.0 0.0 0.0 0.0 0.0 0.0
2.0 0.1 0.1 0.0 0.0 0.0
3.0 0.3 0.1 0.1 0.0 0.0
4.0 0.4 0.2 0.1 0.1 0.0
5.0 0.7 0.3 0.2 0.1 0.1
6.0 1.0 0.5 0.2 0.1 0.1
7.0 1.3 0.6 0.3 0.2 0.1
8.0 1.8 0.8 0.4 0.2 0.1
9.0 2.3 1.0 0.5 0.3 0.2
10.0 2.8 1.2 0.6 0.4 0.2
11.0 3.5 1.5 0.7 0.5 0.2
12.0 4.2 1.8 0.8 0.5 0.3
13.0 5.1 2.1 1.0 0.6 0.3
14.0 6.0 2.5 1.1 0.7 0.4
15.0 7.1 2.9 1.3 0.8 0.4
16.0 8.2 3.3 1.5 1.0 0.5
17.0 9.6 3.7 1.7 1.1 0.5
18.0 11.0 4.2 1.9 1.2 0.6
19.0 12.7 4.8 2.1 1.4 0.7
20.0 14.5 5.3 2.3 1.5 0.7
21.0 16.5 5.9 2.6 1.7 0.8
22.0 18.7 6.6 2.9 1.8 0.9
23.0 21.2 7.3 3.1 2.0 1.0
24.0 24.0 8.0 3.4 2.2 1.0
25.0 27.1 8.8 3.7 2.4 1.1
26.0 30.5 9.6 4.1 2.6 1.2
27.0 34.4 10.5 4.4 2.8 1.3
28.0 38.7 11.4 4.7 3.0 1.4
29.0 43.5 12.4 5.1 3.2 1.5
30.0 48.9 13.5 5.5 3.5 1.6