Splitting 8s Math

I have a question about a few scenarios - mostly splitting 8s, but also splitting splitting 3s against a 7.

From appendix 9 (sorry if a bit hard to read)

6 Decks, Dealer Stands on Soft 17
Dealer Player Stand Hit Double Split
7 3,3 -0.473963 -0.153797 -0.890244 -0.051101
8 8,8 -0.517509 -0.453401 -0.906802 -0.029242
9 8,8 -0.53889 -0.505707 -1.011415 -0.38995
10 8,8 -0.536853 -0.535361 -1.070722 -0.475385
A 8,8 -0.663258 -0.513551 -1.027102 -0.364371

The question is this:

In these scenarios, while you increase your odds of winning... you still have a greater chance of loosing than winning if you split. How do you work the math on this when considering you are doubling your bet on a hand that you have less than 50% chance of winning. That seems counter intuitive.

My analogy (using 8s vs dealer 10): I get stuck with a bet where I have a 75% change of loosing. I am offered the opportunity to double my bet to increase the odds to only a 70% chance of loosing. Do you do it?? I don't think so (throwing good money after bad).

What am I missing?

Here is a rough estimate of the split EV for 8,8 vs T:
The EV of hitting a generic 8 (i.e. 5,3) vs T is -0.249600. So a split 8,8 vs T should be around -0.4992 (since you have two hands).
The actual EV of the split is slightly better if resplits are allowed. Your "-0.475385" thus seems quite realistic.

The intuitive choice is the action which maximizes EV, even if the maximum is negative. You are far better off with two hands of 8s (which have a significant chance to reach 18) than with a single hand of 16 which you are likely to bust (or lose against the dealer).

Quote: MangoJ

Here is a rough estimate of the split EV for 8,8 vs T:
The EV of hitting a generic 8 (i.e. 5,3) vs T is -0.249600. So a split 8,8 vs T should be around -0.4992 (since you have two hands).
The actual EV of the split is slightly better if resplits are allowed. Your "-0.475385" thus seems quite realistic.

The intuitive choice is the action which maximizes EV, even if the maximum is negative. You are far better off with two hands of 8s (which have a significant chance to reach 18) than with a single hand of 16 which you are likely to bust (or lose against the dealer).

Even when looking at it like that, I will loose more money over the long run (GROSS) betting $200 on a 5,3 vs 10 than I will loose betting $100 hand on hard 16 vs 10.

I am looking for some math help on this. I did my own scenarios, and it is a slam dunk. But I am not a statistical expert - I did my best using odds from Wizard of Odds data and my own Excel calculations.

Quote: jdvegas

Even when looking at it like that, I will loose more money over the long run (GROSS) betting $200 on a 5,3 vs 10 than I will loose betting $100 hand on hard 16 vs 10.

I am looking for some math help on this. I did my own scenarios, and it is a slam dunk. But I am not a statistical expert - I did my best using odds from Wizard of Odds data and my own Excel calculations.

By no means am I a mathematician but I am extremely interested in anyone bucking convention and arguing against age-old basic strategy...I hope this conversation continues

Quote: jdvegas

Even when looking at it like that, I will loose more money over the long run (GROSS) betting $200 on a 5,3 vs 10 than I will loose betting $100 hand on hard 16 vs 10.

I am looking for some math help on this. I did my own scenarios, and it is a slam dunk. But I am not a statistical expert - I did my best using odds from Wizard of Odds data and my own Excel calculations.

No you will lose less by splitting. The total wager has already been factored into each option. The results are written in terms of your initial bet. So if you're betting $100/hand, your expectation of hitting 8,8 vs. a 10 is -$53.35 and splitting 8,8 vs. a 10 is -$47.54, so you will lose $5.81 less by splitting on average.

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Quote: jdvegas

Even when looking at it like that, I will loose more money over the long run (GROSS) betting $200 on a 5,3 vs 10 than I will loose betting $100 hand on hard 16 vs 10.

That's exactly what math will do.

If you bet $200 on 5,3 vs 10, you don't lose all $200 in the long run. You lose 24.96% * $200, which is $49.92. Likewise if you bet $100 on 16 vs 10, you lose 53.54% * $100 = $53.54 in the long run.

So what do you choose ? I would take the $200 bet. The 8 vs 10 is a much better hand than the 16 vs 10, to such an extend that it will cover for the increased bet you would need. Still you lose on both hands on the average.

Don't get fooled by the term "throwing up good money at bad money", this is not applicable in splits. You can use the phrase in any doube down decision - you would never double down a negative EV hand. But the split is different, because it *changes* the hand you play to much more favourable values.

Quote: MangoJ

That's exactly what math will do.

If you bet $200 on 5,3 vs 10, you don't lose all $200 in the long run. You lose 24.96% * $200, which is $49.92. Likewise if you bet $100 on 16 vs 10, you lose 53.54% * $100 = $53.54 in the long run.

So what do you choose ? I would take the $200 bet. The 8 vs 10 is a much better hand than the 16 vs 10, to such an extend that it will cover for the increased bet you would need. Still you lose on both hands on the average.

Don't get fooled by the term "throwing up good money at bad money", this is not applicable in splits. You can use the phrase in any doube down decision - you would never double down a negative EV hand. But the split is different, because it *changes* the hand you play to much more favourable values.

I concede. I made a stupid error in my spreadsheet. All is as it should be again.

Thanks all!

But what about surrender vs. hit? Unfortunately, the Wizard's Blackjack Appendix 9 does not have the EV for surrender. I wish this was available. Does anyone know if there is a published table of composition dependent values that include the outcome for Stand/Hit/Double/Split AND Surrender?

I know that my 8,8 vs 10 should be a split and not a surrender. But I do like to to surrender, because I think it reduces my short-term variance. However, it always bothered me that I did not know what the theoretical cost of this decision was. If anyone knows the answer to this, I would be grateful. (Especially if they can point me to an EV table with Surrender values!)

Quote: lajollagamer

But what about surrender vs. hit? Unfortunately, the Wizard's Blackjack Appendix 9 does not have the EV for surrender. I wish this was available. Does anyone know if there is a published table of composition dependent values that include the outcome for Stand/Hit/Double/Split AND Surrender?

I know that my 8,8 vs 10 should be a hit and not a surrender. But I do like to to surrender, because I think it reduces my short-term variance. However, it always bothered me that I did not know what the theoretical cost of this decision was. If anyone knows the answer to this, I would be grateful. (Especially if they can point me to an EV table with Surrender values!)

You're making it too hard! The EV of surrender is a constant -.5:-)

DOOOOH! Of course, you are right.

So in that case, surrender (-0.50000) is worse than split (-0.475385), but better than stand (-0.536853) or hit (-0.535361).

BTW, I did find this old thread helpful, too.