Exploitable Sidebet? - Jackpot Blackjack

Hello all,

As I was playing blackjack at the casino today I encountered a side bet that I thought may be exploitable by counting. Its called Jackpot Blackjack.

You can bet $1-$25 on it.

Payout is as follows using your two cards and the dealers up card.
Three aces suited 250-1
Three aces not suited 100-1
Three Jacks, Queens, or Kings (suited or not) 30-1

If you bet the side bet and lose or push your normal blackjack bet you also lose the side bet. However, if you win your normal blackjack bet you also get paid for the side bet like a normal hand. For example, you put $10 on the normal blackjack bet and $10 on the Jackpot Blackjack side bet and you win your hand. The dealer pays you $10 for your normal bet and $10 for your side bet for a total of $20.

The side bet is just like another normal blackjack bet except you lose on pushes, you cannot double or split, and you get paid 1-1 on blackjacks. But there is always the hope you get 2 aces and the dealer gets one as well. This bet reminded me of the lucky ladies side bet the way the count probably coincides with the normal Hi-Lo strategy.

Is there someone who knows the house edge of this bet or knows how to count this?

Question: if you are dealt a pair of Aces and split them, and one split hand wins and the other loses, what happens to the side bet?

Ignoring that for the moment, if you assume a full 5-deck shoe, there are (312)C(3) = 5,013,320 groups of three cards.
For each suit, there are (5)C(3) = 10 groups of three Aces, so there are 40 groups of suited Aces; this is 1 / 125,333 for something with a 250-1 payout, and even then, you have to win your hand.
There are (20)C(3) - 40 = 1100 groups of unsuited Aces; this is about 1 / 4558.
There are (20)C(3) = 1140 groups of Kings, 1140 of Queens, and 1140 of Jacks, for a total of 3420; this is 1 / 1466.
In effect, this is treating your side bet as a normal bet, but increasing the payout for a win by 222600/5013320, or about 4.4% - but you then have to subtract any advantage you could have gained from doubling or splitting, or a blackjack.

With the sidebet, your basic strategy will change (especially if you sidebet is the same size as your main bet.)

You will double less often. You might also split less often, depending upon what the sidebet payout rules are when you split your hand.

Also, the rule that your sidebet loses when you hands pushes means that you will tend to stand a little bit more often -because hitting your hand produces less equity. I haven't worked the math, but I am guessing that if the size of the sidebet =your main bet then you will:

Stand on 16 vs 10
Stand on 12 vs 4 (and maybe on 12 vs 5)
Stand on 13 vs 2

Something I find unclear based on the OP's description-- Does the 'bonus' payout (like for AAA) supercede the flat win or does the main hand have to win to get paid on all sidebet payouts?

Thank you very much for your input.

You can still lose your regular blackjack bet and win your side bet. If you are dealt two Aces and the dealer gets an ace your side bet would be paid and then the hand would continue to be played out. It's only in the case where you don't win your side bet (right away) then the regular bet determines the side bet payout.

Here's a couple scenarios.
1. You bet $10 on regular blackjack and $10 on the side bet. You are dealt a 19 and the dealer busts. You win $10 from the regular bet and $10 from the side bet for a total of $20.
2. You bet $10 on regular blackjack and $10 on the side bet. You are dealt an 18 and the dealer gets an 18. You push your $10 regular bet and you lose your side bet so you lose a total of $10.
3. You bet $10 on regular blackjack and $10 on the side bet. You bust. You lose both bets for a total of $20.
4. You bet $10 on regular blackjack and $10 on the side bet. You get AA and the dealer gets an Ace (unsuited). You win $1,000 from the side bet and then you continue to play the hand. Even if the dealer has a BJ you still get your money from the side bet.


The guy next to me had $10 bet on regular blackjack and $10 on the side bet. He got a pair of 6s. He split and won one and lost one. His side bet got paid as a win so he ended up netting +$10.

So by your math the side bet is worth playing if 4.4% is greater than the % disadvantage of not being able to double, split, or get 3/2 BJ.

Quote: Mow21

The guy next to me had $10 bet on regular blackjack and $10 on the side bet. He got a pair of 6s. He split and won one and lost one. His side bet got paid as a win so he ended up netting +$10.

Do you remember if that was his first or second hand that won? I believe every sidebet I've seen that is based on player hand resolution has gone to the first hand, but if they're paying out if EITHER of them win, that's another factor in the player's favor.

pwn-ed. {I have been assuming that the bonuses for AAA and other hands get paid immediately - even before the dealer peeks. Otherwise the sidebet would be a terrible bet - with AAA the dealer will have blackjack with a frequency of 4/13 and player would be claiming his bonus payout less than 40% of the time! }

The fact that your sidebet loses when your main bet pushes is a big deal. Normally in BJ you push about 13% of the time. So, ignoring the bonus payouts, I expect that the sidebet will have an EV in the range of -15% to -20%.

Quote: Venthus

Do you remember if that was his first or second hand that won? I believe every sidebet I've seen that is based on player hand resolution has gone to the first hand, but if they're paying out if EITHER of them win, that's another factor in the player's favor.

It was the players first hand that won. And if it would have been the other way around and his first hand lost and second hand won I'm not sure if he would have been paid for the side bet, I'm guessing not.

Quote: gordonm888

I have been assuming that the bonuses for AAA and other hands get paid immediately - even before the dealer peeks. Otherwise the sidebet would be a terrible bet - with AAA the dealer will have blackjack with a frequency of 4/13 and player would be claiming his bonus payout less than 40% of the time!

Correct, the bonuses get paid immediately.

For an 8 deck game, the value of the bonus payouts is:

AAA suited P= 0.0000188 Return = 0.004701
AAA unsuited P= 0.000398 Return = 0.039758
JJJ or QQQ or KKK P= 0.001249 Return = 0.037474

Total Return with 8 decks = 0.081933.

If the first 52 cards out of the 8-deck shoe are all in the range 2-9, then the value of the bonus payouts will rise to 0.122429.

EDIT: I am now estimating that, ignoring the bonuses, the side-bet will have an EV = - 0.145 to -0.155. So, including the bonuses, the house edge on the side-bet with 8 decks is something in the ballpark of 7%.

Quote: gordonm888

For an 8 deck game, the value of the bonus payouts is:

AAA suited P= 0.0000188 Return = 0.004701
AAA unsuited P= 0.000398 Return = 0.039758
JJJ or QQQ or KKK P= 0.001249 Return = 0.037474

Total Return with 8 decks = 0.081933.

If the first 52 cards out of the 8-deck shoe are all in the range 2-9, then the value of the bonus payouts will rise to 0.122429.

EDIT: I am now estimating that, ignoring the bonuses, the side-bet will have an EV = - 0.145 to -0.155. So, including the bonuses, the house edge on the side-bet with 8 decks is something in the ballpark of 7%.

Darn, 7% is pretty high. The count would probably have to be high to consider betting the side bet.

No strategy changes to blackjack.

The wager is settled after the player receives their two cards, and the dealer upcard is revealed. Then after paying/taking the sidebet, blackjack commences.

Quote: SM777

No strategy changes to blackjack.

The wager is settled after the player receives their two cards, and the dealer upcard is revealed. Then after paying/taking the sidebet, blackjack commences.

See rules. Whether or not the player gets a pair of the same rank as the dealer's up card, the side bet remains in play. If the player wins the hand the side bet on that hand wins 1:1, but if that player's hand ties (or loses), the side bet is lost.

Also, when doubling down, the player cannot double the side bet. Since ties lose and the side bet is not doubled down, there are a few changes in basic strategy depending on the relative size of the side bet.

For example, even with a small side bet, the basic strategy becomes stand on 16 vs 10. And with a medium-sized side bet the player should stand on 12 vs 3.

On splits, the side bet is decided by the player's first hand. So the strategies for the side bet hand and the regular hands have differences.

As stated previously, the bonus adds 4.4% to the return.

Getting paid even money instead of 3:2 for a BJ on the side bet costs about 1.2%. In other words 1/4 of a unit about 1 in 21 hands.

Ties happen 8.5 % of the time when hit/stand is the first action and 6.9% of the time when doubling is the first action. I don’t know of a way to get the percentage for the first hand when splitting is the first action, but I’m going to estimate 6%. This number is not that important since ties from splits are a small portion of all ties. Since most ties will come at the 8.5% rate, I’m going to use 8% as the overall tie rate.

So 8% of the time you give an extra half unit to the house, for a cost of 4%.

4.4 % less 1.2% less 4% is a net cost of 0.8%. That added on to an average 0.5% game would be 1.3% house edge. But I assume the only way to get precise figures would be via simulation.

I assumed the bonus pays irrespective of the outcome of the original bet based on the OPs comment, though this is not clear to me based on the rules page (actually I interpret the opposite)

Quote: Ace2

I assumed the bonus pays irrespective of the outcome of the original bet based on the OPs comment, though this is not clear to me based on the rules page (actually I interpret the opposite)

Despite what the rules page may say the bonus pays irrespective of the outcome of the original bet.

It took me awhile to comprehend the side bet because the only thing on the felt was the payout table and I didn't see any rules anywhere. After about a half hour watching I finally picked up on how it was played.

Quote: Ace2

As stated previously, the bonus adds 4.4% to the return.

That 4.4% calculation was done for 5 decks. I reported an 8-deck calculation of about 8% for the value of the bonuses.

Quote: Ace2

Getting paid even money instead of 3:2 for a BJ on the side bet costs about 1.2%. In other words 1/4 of a unit about 1 in 21 hands.

"Blackjack pays 1:1 on the side bet costs the player 2.27% on the sidebet EV. The sidebet also loses another 1.48% of advantage by being unable to receive double payout when the main bet is doubled. So, that is a total of 3.75% lost on the sidebet because of those rules.

Quote: Ace2

Ties happen 8.5 % of the time when hit/stand is the first action and 6.9% of the time when doubling is the first action. I don’t know of a way to get the percentage for the first hand when splitting is the first action, but I’m going to estimate 6%. This number is not that important since ties from splits are a small portion of all ties. Since most ties will come at the 8.5% rate, I’m going to use 8% as the overall tie rate.

I believe that "Player loses 17-21 ties" costs the player 8.86% in House advantage, including doubles and splits. So, i believe that 8.86% should be the overall tie rate, not 8%.

Quote: Ace2

So 8% of the time you give an extra half unit to the house, for a cost of 4%.

You have made a math error. Increasing the player's loss probability by 8.86% will reduce the house edge by 8.86%, not by 4.43%.

Quote: Ace2

4.4 % less 1.2% less 4% is a net cost of 0.8%. That added on to an average 0.5% game would be 1.3% house edge. But I assume the only way to get precise figures would be via simulation.

I continue to get that, ignoring the bonuses, the sidebet rules represent a disadvantage of about 12.6% in EV as compared to the main blackjack EV. I also believe that the value of the bonus payouts is dependent upon the number of decks.

Quote: gordonm888

That 4.4% calculation was done for 5 decks. I reported an 8-deck calculation of about 8% for the value of the bonuses.

Actually I did an infinite deck calculation which gave 4.5%. That was close enough to 4.4 % so I went with that. Apparently you’re forgetting that the bonus is on half of the total bet, not the entire bet. Besides, intuition will tell you that the number of decks isn’t going to cause a variation anywhere close to 82% relative

Quote: gordonm888

Blackjack pays 1:1 on the side bet costs the player 2.27% on the sidebet EV.

Again the 1:1 cost is on half the bet. 2.27 % / 2 is 1.14 % but I’ll stick with my 1.2% since this can easily vary 6 basis points just by a one deck difference. This calculation is not that precise anyway.

Quote: gordonm888

The sidebet also loses another 1.48% of advantage by being unable to receive double payout when the main bet is doubled.

Nope. You lose 1.48 % in a game that doesn’t allow doubling (and you play the hand out taking as many cards as needed). This game does allow doubling, but half the bet pays 1:1 if won, and a loss if tied. Totally different scenario.

Quote: gordonm888

I believe that "Player loses 17-21 ties" costs the player 8.86% in House advantage, including doubles and splits. So, i believe that 8.86% should be the overall tie rate, not 8%.

This game is not the same as a game where player loses ties. These are not 2 independent hands played at different rules. It’s one normal BJ hand where 1/2 of it has different payouts in a few cases.

Quote: gordonm888

You have made a math error. Increasing the player's loss probability by 8.86% will reduce the house edge by 8.86%, not by 4.43%.

Negative. See above.

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