Pokerstars have an offer where they will add 30% to your net blackjack winnings at the end of the week. You must make at least 100 bets. The amount they add is from $3 to $1500 (so I assume your net winnings must be at least $10).

This seems plus EV to me.

If I play 100 hands at $5 each, my negative EV from normal play is about minus 3 dollars. My standard deviation is $50 (and apparently that means absolute average deviation of about 80 percent of that) and close to half the time that will be positive, leading to a gain of 12 dollars half the time or 6 dollars of EV on the bonus. So the net profit over 100 hands is $3, or +EV = 0.6 percent.

Is that right?

(I think you can improve on the strategy too - if you get to the 80th hand and you are behind can no longer catch up and get the bonus you can just stop playing already).

Or you make 99 min bets and 1 max bet .

^ Bingo.

It does say "Any individual bet in excess of $50 does not count towards this promotion."

So I do 99 x 0.10 and 1x $50.

I'm thinking - what if I lose the first big bet?

Presumably it's plus EV to chase it - because while the immediate bet is slightly -EV, you are giving yourself a 50-50 chance for a big +EV bet on the next hand. - this could be dangerous lol.

Let's suppose you lose a little on your first 99. You then bet $50 and win. If you then reduce your bet (so you don't blow it all at once) - wouldn't every bet after that be +EV, since once you are in the black (and fulfilled the requirement) you'd be getting a payoff of 130% on any win?

@VBAces - No, because if you lose you also bonus on your stake which comes from the in black money. So a $50 nominal bet can potentially cost $65.

However......

If we stop playing at -150, - 100, -50, 0, 50, 100, 150 we get -150, -100, -50, 0, 65, 130, 195 respectively - so these positions are worth at least this much.

That means that when we are on zero, we have the option to "stop" (EV 0), or to take a 50.3-49.7 percent flip to go up to a position worth (at least) 65 dollars or down to one worth 50 dollars*. The EV of the "play" strategy then is (at least) 7.155 dollars so the zero position is worth at least 7.155.

Now, taking the -50 position (i.e. we have lost net one bet so far). If we play we are flipping between going down to -100, or going up to a position we have calculated as worth at least 7.155. The EV of "play" from -50 then is at least =-46.74 so we should chase after we lose the first bet. Similarly, the EV of "play" when we have won net one bet and are on +50 is between going up to a position worth 130 or down to one worth 7.155 - EV = 68.21 - again beating "stop" which has EV of 65.

Basically we keep iterating (manually but I did it a high number of times and we were tending towards a solution) and we find:

First column is net winnings pre bonus. Second column is calculated value of the position, third column is the calculated value of the play strategy - where it is lower than the calculated value of the position - the strategy is "stop" - where it is higher, the next iteration would be to copy it to the second column.

-650 -650 -650.3
-600 -600 -600.3
-550 -550 -550.2418011182
-500 -499.8828996342 -499.8828763389
-450 -449.1607169796 -449.1421266282
-400 -397.7887889582 -397.7887283328
-350 -345.7965547124 -345.7602483564
-300 -293.1035966004 -293.1035216081
-250 -239.7743553074 -239.7226891196
-200 -185.697344124 -185.6972777136
-150 -130.9673581367 -130.9042716303
-100 -75.449713352 -75.4496676026
-50 -19.2617433798 -19.1925958519
0 37.7436820205 37.743707172
50 95.437352298 95.5062748629
100 153.9662028302 153.9662139135
150 213.2016613836 213.2638584767
200 273.2773811935 273.2773850763
250 334.0783690149 334.1278634306
300 395.7129591355 395.7129601958
350 458.0916309482 458.1235764952
400 521.2876419518 521.2876421671
450 585.2465830988 585.2576839018
500 650 649.7340312987
550 715 714.61
600 780 779.61
650 845 844.61
700 910 909.61

So the total value of the offer was tending towards 40 dollars. The correct strategy then is to play till you lose $550 or win $500.

If you set a stop win/loss at $200 then it seems to tend to about $25 of EV.

* So I'm modelling blackjack as a single coinflip rather than taking account of doubles, splits, BJ paying 3 to 2 etc.

Second week started. Won just over $15 this time. Still waiting for the bonus to be credited from last week but it should be within 48 of the end of the week Eastern Time so that's nothing unusual yet.

Nice bit of Midas touch in on of the 99 min-bet hands though

Hand# 935165882: Blackjack Table 'Classic' - 2015/06/22 14:02:22 CET [2015/06/22 8:02:22 ET]


*** BETTING ***
Seat 3: lektoraj bets $0.10


*** INSURANCE ***
Seat 3: lektoraj [Ah, As] declines insurance

*** STARTING HANDS ***
Seat 3: lektoraj [Ah, As]

Dealer: [Ac]

*** PLAYING ***
Seat 3: lektoraj
Starting Hand: [Ah, As]
Split:
Seat 3: lektoraj Hand: [Ah, 8h]
Seat 3: lektoraj - Stand on 19.
Seat 3: lektoraj Hand: [As, 8h]
Seat 3: lektoraj - Stand on 19.
Dealer:
Starting Hand: [Ac, Qh], Stand on 21


*** SUMMARY ***
Dealer: [Ac, Qh]

Stand on 21
Seat 3: lektoraj [Ah, As]Split: 1 (2 hands)
Hand1: [Ah, 8h]
Stand [Ah, 8h]
Result: LOST (bet: $0.10, paid: $0.00)
Hand2: [As, 8h]
Stand [As, 8h]
Result: PUSH (bet: $0.10, paid: $0.10)

Result: (bet: $0.20, paid: $0.10)


Being a good boy I have reported the bug though.

Lektor -- good calculations. The +EV from this promotion comes from being near that zero flip point. So it makes sense that if you're too far down to break even, you should quit. Or if you're so far ahead you won't lose it all back, you should quit.

Not sure how much accuracy is lost by modelling BJ as a coinflip instead of accounting for splits, doubles, etc. If you're not varying bet size it shouldn't matter.

This is a cash money bonus and not a bonus that has additional cash-out requirements, right?

I didn't look over your model but blackjack is nothing like a coin flip. Playing perfect basic strategy you will only win about 42% of hands (because dealer goes last). The house edge is much smaller than that implies mainly because of paying 3:2 and allowing doubling.

Well yes, obviously. The question is whether that discrepancy will affect EV on this promo.

Ok - so I found out that the push in post 6 is because of the OBBO rule - against dealer blackjack you only lose your original or busted bet.

They also paid me the "winnings boost bonus" for week one about lunchtime (CET) today (Tuesday). They said "at least 30%" and they seem to have paid me about 33% so the offer is legit.

I am aware that modelling a hand as a flip is a simplification. What I really need is something like this:

http://wizardofodds.com/games/blackjack/appendix/4/

for the specific rules for the PS double-deck game. They have lots of specifics at PS. For example the ten cent game pays 3 to 1 for 7-7-7. Now I understand more about the rules I have put them into the wizardofodds calculator and this form has a 0.23 % house edge only, so it may be the case that you can keep playing for a lot longer than I calculated above.

Yes - there are no additional playthrough requirements (other than the original 100 hands) - the money is just in my main pokerstars account.