boomdog
Joined: Jan 9, 2010
• Posts: 23
March 3rd, 2010 at 4:50:44 PM permalink
I know what the chart says but I cant make myself split if I have a big bet already. My question is what is this doing to the house edge?
pocketaces
Joined: Nov 11, 2009
• Posts: 158
March 3rd, 2010 at 5:09:19 PM permalink
The best advice would be to bet at a level where you are always comfortable with splitting and/or doubling.

For loss in EV, as always you can consult the Wizard's blackjack appendix 9. EV comparisons are:

88 vs 9 - Split: -0.389950 Hit: -0.505707
88 vs 10 - Split: -0.475385 Hit: -0.535361
88 vs A - Split: -0.364371 Hit: -0.513551

(Assuming 6 decks, S17, DAS allowed)

As you can see, you are giving up quite a bit by not splitting 8s vs 9 or Ace (approx. 11-15 cents per dollar bet), and a smaller amount by not splitting 8s vs 10 (approx 6 cents per dollar bet). In terms of total house edge, the increase will be small simply because these hands come up very infrequently. But, when you are faced with the decisions, it is not borderline - you are giving up a lot by deviating from basic strategy and choosing the wrong one.

If you must avoid splitting 8s in certain situations, I would restrict it to versus an upcard of 10 only.

Also note that if surrender is allowed, your second best decision will always be surrender. This is less of an expected value loss in the differentials between the decisions.
Wizard
Joined: Oct 14, 2009
• Posts: 22046
March 3rd, 2010 at 5:21:23 PM permalink
Let's assume six decks and the dealer stands on soft 17. We can solve this problem by taking the sum for all three situations of the probability it happens by the effect of the mistake. My blackjack appendix 9 shows both. Assuming the player chooses to hit instead, the effect on the expected return of the game is:

Prob(8,8 vs A)*(EV(hit)-EV(split)) + Prob(8,8 vs 9)*(EV(hit)-EV(split)) + Prob(8,8 vs 10)*(EV(hit)-EV(split))

= 0.0003036 * (-0.513551 -(-0.364371)) +
0.0004404 * (-0.505707 -(-0.38995)) +
0.0016249 * (0.535361 -(-0. 475385)) = -0.019%.

If the player surrenders instead of hitting the effect drops to -0.013%.
It's not whether you win or lose; it's whether or not you had a good bet.