Value of Pushing on 22?
Thanks.
Quote: MrGoldenSunHello. I have a coupon that allows me to push a hand of 22. I can hold onto the coupon until my first 22. It doesn't apply to doubles or splits. What is the value of this?
Thanks.
One betting unit. It turns a sure loss (-1 unit) into a sure push (0 units).
Quote: unJonOne betting unit. It turns a sure loss (-1 unit) into a sure push (0 units).
If you offered to simply pay me one unit, I think that's better than the coupon, because I don't have to play any -EV hands to get that unit. So my intuition is that the value is less than one unit. The fact that the 22 might take a while to happen makes it less valuable...right...?
Quote: MrGoldenSunIf you offered to simply pay me one unit, I think that's better than the coupon, because I don't have to play any -EV hands to get that unit. So my intuition is that the value is less than one unit. The fact that the 22 might take a while to happen makes it less valuable...right...?
But if someone was definitely going to play blackjack anyway , with or without buying the coupon , then wouldn’t the prior -EV hands necessary to use it not matter ?
Quote: mcallister3200I believe something like 4.x% percent iirc. Would be worth close to 6% if you could double according to blackjackreview.com. Definitely hit your 12 vs 4-6 with the coupon if you’re going to leave once you use it.
The answer above seems to be the most correct so far. If I were to guess, I would say the value of the coupon is 3.75%^^^ (or more) based on the limited information I have found so far.
^^^: Until you have a better answer/ reply, I would use 3.75% as the "rough value" for the coupon.
Also, it was quite hard for me to find anything about "% of hands where a player busts on 22", but here is a link below that may be of some use:
https://www.blackjacktheforum.com/entry.php?55-Player-Bust-Rates ***
***: The actual value for you could likely be less than the % figure in the above link, because with that figure "...split hands count...".
Lastly, paraphrasing what mcallister said, you should hit H12 vs "everything" while you still have the coupon (there may be some other BS exceptions, but generally play BS for all other hands, IMO).
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Update (about 1050 pm):
Some of my reply above was still being written/re-written, so that is why my post above may look a bit different to anyone quoting an earlier version of it (see post below, for one example of this).
Quote: ksdjdjI think the answer above is the most correct so far. It was hard for me to find anything about "% of hands where a player busts on 22", but here is a link below:
https://www.blackjacktheforum.com/entry.php?55-Player-Bust-Rates
Note: The actual value for you will be less than the % figure in the link/graph because with that figure "...split hands count...".
Lastly, paraphrasing what mcallister said, you should hit H12 vs "everything" (while you still have the coupon).
What would you do with A-A v dealer A or dealer 10?
Quote: michael99000What would you do with A-A v dealer A or dealer 10?
If it is a game with "American" hole card rules, I would:
1) split A-A v dealer A
2) split A-A v dealer 10
Note : This is correct for both S17 and H17 "dealer rules".
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Update (1110 pm):
I used "infinite deck", and can not DAS or re-split A's.
S17: for hitting AA with this coupon, it costs a BS player less than 15.5% in EV vs a dealer 10 and that it costs a BS player less than 3.5% in EV vs a dealer A.
H17: for hitting AA with this coupon, it costs a BS player less than 7.25% in EV vs a dealer A (for "vs a dealer 10", the answer is the same as it is for "S17" above)
Quote: MrGoldenSunIf you offered to simply pay me one unit, I think that's better than the coupon, because I don't have to play any -EV hands to get that unit. So my intuition is that the value is less than one unit. The fact that the 22 might take a while to happen makes it less valuable...right...?
I agree with this. On a related note, I used a push on 22 ACG coupon at The D last year. Took over an hour to get a 22. I think I won about $300 flat betting $25/hand (the coupon limit). I expected it to take 5 minutes or so.
Quote: MrGoldenSunHello. I have a coupon that allows me to push a hand of 22. I can hold onto the coupon until my first 22. It doesn't apply to doubles or splits. What is the value of this?
As others wrote, a quick answer is the value of the maximum you're allowed to bet. Just wait for a 22 and then play it, resulting in walking away from the table with an extra unit.
A more rigorous answer should look at the cost of waiting for that 22. This is something I don't know exactly, but can estimate.
The cost to the player of the dealer-push-22 rule is 6.91%. However, the dealer will get to 22 more than that, because the player won't care if he busted first. Depending on the rules, the player will bust about 15.7% of the time. If we assume this is uncorrelated with the dealer's probability of busting (which it's not) the probability of a dealer bust is 6.91%/(1.0-0.157) = 8.2%.
I know this is rough, but let's assume the player's 22 probability is the same. I know the dealer will bust more than the player, but this coupon also doesn't count after a split, so let's just say those factors offset. So, if the player gets a 22 8.2% of hands, then he will bet a 22 once every 1/0.082 = 12.2 hands on average.
Let's say the house edge in the base game is 0.75%. The cost of playing 12.2 hands at that house edge is 12.2*0.0075 = 0.0915. So, subtract that from the one unit value and you get a value of the coupon of 1.0 - 0.0915 about 91% of face value.
Quote: WizardAs others wrote, a quick answer is the value of the maximum you're allowed to bet. Just wait for a 22 and then play it, resulting in walking away from the table with an extra unit.
A more rigorous answer should look at the cost of waiting for that 22. This is something I don't know exactly, but can estimate.
The cost to the player of the dealer-push-22 rule is 6.91%. However, the dealer will get to 22 more than that, because the player won't care if he busted first. Depending on the rules, the player will bust about 15.7% of the time. If we assume this is uncorrelated with the dealer's probability of busting (which it's not) the probability of a dealer bust is 6.91%/(1.0-0.157) = 8.2%.
I know this is rough, but let's assume the player's 22 probability is the same. I know the dealer will bust more than the player, but this coupon also doesn't count after a split, so let's just say those factors offset. So, if the player gets a 22 8.2% of hands, then he will bet a 22 once every 1/0.082 = 12.2 hands on average.
Let's say the house edge in the base game is 0.75%. The cost of playing 12.2 hands at that house edge is 12.2*0.0075 = 0.0915. So, subtract that from the one unit value and you get a value of the coupon of 1.0 - 0.0915 about 91% of face value.
Thinking about this more. I think the other way to get to an accurate answer is to figure out the Player Edge for a blackjack rule that has player push 22 with appropriate tweaks to BS. Then multiply that Player Advantage times the expected number of hands the player will play with that push 22 rule (call it 12.2 hands per the Wiz calculation above).
Good variance!
