odiousgambit's Blog

Apparent Edge vs EV

I redid the previous blogpost, “second chance parlay betting“, so that any suggestion that the HE can be changed by a betting system is not stated. When a parlay bet is calculated for ‘edge’ using the initial bet in the normal way, it gives the appearance that such edge is indeed changed. Typically, with the assumption that each leg is -EV, the end result of a parlay bet can be shown to indicate the total EV is even of greater magnitude in the negative. Likewise, if all legs are +EV, even greater player increase in EV can be shown. However, the ‘edge’ is not changed by the process, the EV of the parlay is changing because of the increase in the amount bet that a parlay method entails. So I am saying this an ‘apparent’ change in edge even though the increase in EV, negative or positive, is very real.

I have to note that Wong and the Wizard in some of what they have written both either encourage or do not discourage parlay betting where the legs are believed to be +EV. I can’t find where they say why they like it other than the obvious result of sometimes getting a nice payoff if you can handle the risk.

I’ve decided to even go so far as to use the phrase “Deceptive Apparent Edge” from now on … so that anyone reading what I have written is not put off by thinking that I am claiming a parlay system can affect the house edge. The previous blogpost has been rewritten with this change. Where I am claiming something is +EV, this is due to the nature of the offer, such as second chance betting.

Second Chance Parlay Betting

I’m seeing offers in online sports betting where you get a second chance type bet of the ‘get winnings only type’ that I’ll call winnings-only freebet [WOFB]; and, significantly, you get the WOFB ‘win or lose’ in the offers I am interested in… but they often make you do a 3 leg parlay to get the second chance, sometimes a same game [SGP].

I want little to do with SGPs but if you get the entire first wager back as a WOFB , and it’s 2 legs, I have done those.

Mainly though, I seek and take advantage of win-or-lose WOFB offers with initial bet a 3-leg parlay [with SGP not necessary in the offer]. However, the WOFB may be half the initial bet. I have been running bad on those, certainly you need to win the initial bet at least sometimes on these or decline in bankroll will happen. At least, this has developed as my gut feeling.

So …

I have wanted to check the math for myself for sometime now. A normal parlay with each of the 3 legs at -200 [typical for me] results in a +237 bet, reflecting winnings but not chances of winning. Returns 2.37 per unit, total in hand 3.37

+237.5 should be the payoff, cheating me out of half a penny per dollar bet, but the big deal with parlays is that the Deceptive Apparent Edge [DAE]* for the online sportsbetting site is increased, as I will show below.

Disclaimer: mistakes possible, I appreciate any help

At -200 with a fair bet each leg wins 2 times out of 3
2/3*2/3*2/3=8/27 for the chances of winning

the parlay payoff works like this, using one unit

1*100/200=0.5 first payoff on first leg win
next bet use 1.5
1.5*100/200=0.75
next bet use 2.25
2.25*100/200=1.125

final amount 3.375
winnings 2.375

____

if a fair bet,
8/27*2.375 chances of winning times amount to win
-19/27 *1 chances of losing times amount to lose
8/27*2.375-19/27*1=0 or no advantage long run, so this seems to be correct

HOWEVER

if true chances each leg not 0.667 but 0.633 [say]
betting only one bet [no parlay] at -200, one unit
chances of winning times amount to win minus chances of losing times amount to lose
0.633*0.5-0.367*1= -0.0505 or HE 5.05% [per leg]

chances of winning 3 legs

0.633^3=0.2536 [so chances of losing 0.7464]
0.2536*2.375-0.7464*1= -0.1441 or DAE 14.4%

thus a demonstration that the negative EV increases
definitely gets worse if each leg more than 5% HE

>>>>

BOOSTS

what if there is a 30% boost to winnings?

0.2536*[2.375*1.3]-0.7464*1

= 0.03659 or 3.7% apparent edge

this is not a 15% edge , which you might think taking 30% - roughly 15%, note well, and edge will be very slim or absent if greater than 5% HE each leg, or any leg!

if a 50% boost,

= 0.15705 ........... allows larger edge per leg

>>>>

What about +EV if you get win or lose second chance bet?
let’s say made at +200, the least I would pick

I ascertain it as simple as adding the EVs of the two phases together. For any bets that are made independent of each other, the total EV of all that action is the sum of the EVs added together. I can’t see how this is any different than, say, Craps bets … as long as you can say any such bet has an EV.

EV of second chance bet is chances of winning times amount to win minus nothing, with nothing at risk. Fair bet at +200 is 1/3 chances of win, with amount to win 2 units

however, we know these are not fair bets.
so say actual chances are 0.300 instead of 0.333

chances of winning times amount to win, nothing further now at risk
0.3*2 = 0.600
the EV of first phase is -0.144, add to that 0.600 to add EVs
-0.144+0.600=0.456……… nicely +EV

I do wonder if I’m making an error … 45.6%. On the other hand, it is rare to see this offered.

Instead, you often only get half the initial wager back as a second chance
still, it’s the generous 'win or lose' that I’m investigating here

chances of winning times amount to win
0.3*0.5*2=0.3

adding the EVs,
-0.144+0.3= 0.156
now it is +EV but 15.6% DAE…

with true probability unknown, I did conservative second phase
but even if the first phase is -25% HE … this is nicely +EV

>>>>

Further investigation: I frequently use alternate game total bets to get down to -200 or -300
this gets the HE on one bet up to 7.5% when I check ; let's use 8% which may be possible sometimes

How much does the vig increase in a 3 leg parlay using -300 legs?
-300 implies 3/4 chances of winning, 0.75 if fair

actual chances with 8% vig = 0.69
checking that: pays 1/3 times one unit

chances win * amnt - chances loss * amnt
0.69*0.33-0.31*1=-0.0823 …………….. so 0.69 is correct

parlay 3 legs at -300 with prob. of winning ea 0.69
site should offer +137, payoff 1.37 per unit

parlay 3 legs
0.69^3=0.3285 chance of winning
0.6715 chance of losing

chances win times amnt - chances loss times amnt
0.325*1.37-0.6715= -0.22625 … 22.6% DAE

what if get only half of orig wager win or lose?

Fair bet at +200 is 1/3 chances of win, with amount to win 2 units
instead of 0.333 chance of winning, being conservative use 0.300 again

at usual formula,

0.3*0.5*2=0.3
again adding the EVs together we get 0.30-0.23= +0.07
7% +EV ...................... hardly marginal

Conclusions: still well worth suffering through the losing streaks I seem to get on initial bet
winning initial "sometimes" is so essential a lower than ideal payoff for that initial bet is best for morale [not EV]
+200 is really not enough for the WOFBs. Those closer to +300, even going over that, up to +320, I think is the way to go

*I’m trying now to avoid saying the House Edge or Player Edge is changing, in respect to the Wizard, who is always pointing out that a system of betting can not change edge. The next blogpost is about that

Dealer's Choice 3 Card Poker

Aside from the common goal of just having fun, I have long realized the idea with “dealer’s choice” poker in home games is to call a game that you think you play better than the other players, when it is your turn. Likewise, you’ll want to observe more caution in those games you haven’t figured out.

Only recently, though, have I concluded that other players often won’t play 3 card poker games well.

Correct play is less intuitive. To be dealt 3 cards, with no draw, a high pair is a good, likely winning hand as you can see from the Wizard’s page on 3 card guts [depending on # of players]. However, often it’s expected for a home game to have a draw. A draw changes everything. If you start with a pair, it’s very hard to improve that, and in my experience, if the table has at least 6 players, a pair loses way too often to a better hand. Another factor is that a straight is harder to get than a flush with 3 cards, so “a straight beats a flush” and this rule will not change if there is a draw! If a player gets to see 5 cards altogether, the chances of getting a straight are better than getting a flush, if we can go by the known chances of getting these two hands after being simply dealt 5 cards.

I recently found a website that confirms things I have noticed. It describes a ‘drop’ game we don’t play where I play, but a lot of it applies to what we do. I’ll quote some of it, emphasis mine

http://www.homepokeredge.com/3-card-drop-w-draw-tips.html

Quote:

The probabilities below are the chances for an individual player being dealt these hands in the initial deal. For an 8 player game expect that at least one player will be originally dealt a pair or better almost all the time, a flush or better over 50% of the time, a straight or better nearly 30% of the time.
Never play a hand that is not either a pat hand or a one card draw hand.

3 Card Hand [when dealt 3 cards, before any draw, + probability]

Straight Flush ………… 0.22% [note the decimal point]
3 of a Kind ……………. 0.24% [note, not much difference]
Straight ………………….. 3.26%
Flush ……………………….4.96% [causing the straight to be higher ranking]
Pair …………………………16.9% “

OK, so maybe none of this is a surprise. This is next, credit to same site. I made a table.

“PROBABILITIES of ONE CARD DRAW to HANDS

Approximate chances of improvement when holding these hands and drawing one card."

Holding	Drawing one card to	No. of cards to make hand	Probability
Pair	Three of a Kind	Two	4%
2 to Flush	Flush	11	22%
2 to Straight [open]	straight	8	16%
2 to Straight [inside]	straight	4	8%
2 to Straight Flush [open]	Straight Flush	2	4%, but 18% chance of making a flush + 12% chance of making a straight
2 to Straight Flush [inside]	Straight Flush	1	2%, but 20% chance of making a flush + 6% chance of making a straight

Holding a pair, you have made it impossible to get a straight or a flush. This is also why a suited AK in many games is almost as good as holding a pair of Aces and much better than low pairs. In 3 card poker, holding a pair you can only improve to 3 of a kind and there are only two cards that can make that happen. So this is one area where intuition can fail you very quickly. You should discard so that you no longer have a pair, even a pair of Aces, if you can keep 2 to a straight or 2 to a flush, and probably fold if you can't do this [depending on no. of players?] And drawing one card to an open straight is the hand to be hope to be playing [outside of pat hands] ... drawing one to an open straight flush even more so of course.

Losing Streaks, Hard to Take

Ultimate end of AP for online gambling? That will be AI, and that might be soon

End of online sports AP for the guy, now, who understands what to do, yet stops? That might be the guy who abandons +EV due to ability to tolerate losing streaks, or perhaps you can say lack of understanding of risk of ruin, or just real acceptance of it and the very same occasional losses that you actually predicted!

I used Act/Warhorse* site to generate 500 rolls of a 4 sided die to simulate the usual max level I’ll ‘go for’, which is less than +300. Yes I’ve said I’ll go up to +400 but that’s not usual. So 1/4 actual chances will be similar to the outcome expected betting at, say, +280 or whatever, what with house edge. Prior to the rolls I sought to find out how long the worst losing streaks would be on rolling a 4.

The worst was 14 rolls with ‘no 4’ , which occurred twice. Several others close to that. The max bet that I am doing these days is $50, and I have to tell you those kinds of losing streaks are hard to take. For that reason I aim for ‘more like +200 or so’ which gives up some EV.

Under the assumption that I am making about the HE to be encountered, and assuming I understand the math of the second chance bet, I’m vowing to stick with it through losing streaks. I’m bracing myself, though.

I posted the roll results below [now removed as of 9-20-25]

* this online dice roller has features hard to find: it sends you the results in an email, and you can have the same email sent to others simultaneously. You have to sign up, which is free ………… http://acts.warhorsesim.com

asterisks indicate streaks with 'no 4' , notable ones can be found using search for the 'equal' sign, =
there are 131 '4s' out of 500 [edit], expected was 125 of course

dice results removed now

Quit Counting Outs UTH!! Saved Charts

you may need to read the starting thread https://wizardofvegas.com/forum/gambling/tables/37935-quit-counting-outs-uth/

Although the charts are pretty much in final form, some edits for clarity continue.

In the below, the charts are for the 1x decision point when all the player has is a kicker. It's important to follow the Wizard/Grosjean advice to fold in the face of, on the board, 4 to flush and 4 to open ended straight. It's a simple strategy that has exceptions. As a matter of practice, with a Q,4 or K,3 [or less] against a board 3-to-straight fush, and [adding on 3-3-23] Q,2 where Q not top kicker, I fold at 1x/river decision pt.

The charts are very wordy in order to provide clarity. You can familiarize yourself with them and then you can make strategy cards to take to the table. What would work for me as small strategy cards are the two charts at the bottom.

In the case of the second chart, exceptions are more rare and I am trying to identify them. The use of the word 'then' is to indicate you take the process in steps.

Player Kicker in Play	Permissible Missing Cards Outranking Kicker
Unpaired Board	One Card Can Be Missing, Bet 1x
Board has One Pair	2 Cards Can Be Missing, ditto
Board has Trips	3 Cards Can Be Missing, ditto
Board = Two Pair, Fifth Card Makes Dealer Outs	3 Cards Can Be Missing, ditto
Board has Two Pair, Fifth Card Lower in Rank	4 Cards Can Be Missing, ditto
Board has 4 OAK	play 7-card or better player kicker, ditto

Player Kicker Can’t Win	Action Indicated
The board doesn't have a pair or better	No Pair means No Play, instant fold
Board Has One Pair	A 9-card or lower in the other 3 cards = instant fold then a 10-card in the three folds UNLESS ALL other 4 cards higher then a qualified 10, or Jack* or higher in the three, plays *known exceptions 9,9,10,A,J + 9,9,10,K,J
Board has 2 pair with the Fifth card making dealer outs.	A 10-card or lower as the fifth card means instant fold. Play a Jack if Middle Value Play All Higher Others
Board has two pair, AND fifth board card lowest in rank	An 8-card or lower anywhere on the board is an instant fold. Play all that have higher fifth cards
Board has Trips	A 9-card or lower in the other 2 cards is an instant fold Then 10-card there is a fold unless ALL other 4 cards are higher Then a qualified 10, or Jack or higher in the two, plays
Board has 4 OAK	An 8-card or lower as the 5th card is an instant fold A 9-card as the fifth card is a fold UNLESS the 4OAK cards are higher Play All Others

>>>

My choice for a strategy card with abbreviations and memorized parts omitted

Kicker in Play	# Cards
Bd Trips/2 pair 7-O	3 Cards
Bd 2 Pair 4-O	4-O=4 cards
Bd 4 OAK	play 7-card+

in the above, don't need to know what I'm looking for or what to do. 7-0 or 4-O indicates the type of 2 pair board by initial outs. 4-O=4 cards is a mnemonic

Kicker Gaffed	FOLD
Bd = One Pair	Pert 9-card 10-card unless all higher
Bd 2 pair 7-O	Pert 10-card Play Pert Jack if Middle Val Play all Pert Queen+
Bd 2 pair 4-O	8-card anywhere Play all higher Perts
Board = Trips	9-card 10-card unless ALL higher
Bd = 4 OAK	Pert 8-card 9-card UNLESS all 4 higher

although in some ways easier table, I don't have it memorized as well. Leaving what to do in there for now. I know what 4 I'm talking about in the 4-OAK section. Pert means Pertinent